Exhibit J

BBVA Banco Francés

In the City of Buenos Aires, on August 3, 2009

Telefónica S.A
Distrito C. Edificio Central
Ronda de la Comunicación s/n,
28050 Madrid
ESPAÑA

Dear Sirs,

          Pursuant to our previous conversations, we hereby offer you a proposal of terms and conditions (the “Proposal”) under which BBVA Banco Francés S.A. shall be able to act as Escrow Agent (“BBVA Banco Francés” or the “Escrow Agent”) in the purchase of the remaining shareholding in the capital stock of Telefónica de Argentina S.A (“TASA”), in accordance with the provisions established in Executive Order No. 677/01 (the “Executive Order”), by Telefónica S.A. (“TESA”). At present, TESA holds 98.2% of TASA’s capital stock.

          Such procedure known as “Régimen de Adquisición de Participaciones Residuales” (Squeeze-out Procedure) (the “Acquisition” or the “Tender”) grants to the controlling company that holds more than 95% of another company’s capital stock, the right to buy, at a fair price, the remaining minority shares upon a minority shareholder’s demand in this regard. TESA has received such demand last April 27, 2009.

          Such procedure establishes that the controlling shareholder must accept the demand and issue a Unilateral Declaration of Intent for the Acquisition of 100% of the Remaining Shares held by Third Parties (“Declaration of Acquisition”), and that such issuance of Declaration of Acquisition has to be approved by TESA’s Management Council at a duly held meeting. Such Declaration of Acquisition was approved by TESA’s Management Council at the meeting held on June 23, 2009 and was published in the Daily Gazette of the Buenos Aires Stock Exchange on June 23, 24 and 25 and in the newspaper La Nación on July 1, 2 and 3, 2009.

          Pursuant to the provisions set forth by the Executive Order, no later than five days after having obtained the acceptance of the Comisión Nacional de Valores (Argentine Securities and Exchange Commission)

(hereinafter, the “CNV”) of the fair price per share of TASA offered by TESA in the Declaration of Acquisition (the “Price”), TESA shall deposit the amount equivalent to the Price for all the shares set forth in the Declaration of Acquisition in an account opened for such purpose with the Escrow Agent, along with a list of the minority shareholders provided by Caja de Valores S.A., so that the Escrow Agent may start liquidation of the payment demands made in due time and manner (the “Transaction”).

1 Appointment

Subject to the acceptance of this Proposal, TESA appoints BBVA Banco Francés to act as Escrow Agent for the Transaction. It is hereby expressly stated that BBVA Banco Francés shall, under no circumstances, provide advice as regards issues concerning the relationship between TESA and/or TASA and the ADRs’ shareholders and/or holders of TASA, including, but not limited to, the regulatory and/or contractual issues applicable by the Securities and Exchange Commission or related to the ADRs program.

2. Services to be provided by BBVA Banco Francés

In its capacity as Escrow Agent, BBVA Banco Francés agrees to perform the following acts and render the following services:

a) Opening a remunerated special account in the name of TESA for exclusive purposes of the Transaction on the account and order of BBVA Banco Francés (who shall act under the provisions hereof), pursuant to Section 28 of Executive Order No. 677/01, last paragraph, under the name of TELEFÓNICA S.A.- ADQUISICIÓN RESIDUAL ACCIONES TELEFÓNICA ARGENTINA S.A. — ORDEN BBVA BANCO FRANCÉS S.A. TELEFÓNICA S.A.- ACQUISITION OF REMAINING CAPITAL STOCK IN TELEFÓNICA ARGENTINA S.A. — TO THE ORDER OF BBVA BANCO FRANCÉS S.A. (the “Account”). Additionally, if TESA so requests, the Bank shall open one or more accounts in Argentina or abroad for purposes of the Transaction. Within five Business days from the granting of such administrative acceptance to the Acquisition by the CNV, TESA shall deposit the amount resulting from multiplying the Price by 100% of TASA’s shares under the Tender, and shall simultaneously file, within the same term, a list of the minority shareholders along with their personal data specifying the number of shares and values held by each of them.

The money deposited in such account, the beneficiaries of which shall be all minority shareholders who are included in the list mentioned above, shall accrue interest at the rate paid by the Escrow Agent applied to deposits in

savings accounts, daily published by BBVA Banco Francés at its offices, and informed by BBVA Banco Francés to Banco Central de la República Argentina (Central Bank of the Argentine Republic).

b) Upon compliance with all the requirements set forth in section 29 of Executive Order No. 677/2001, BBVA Banco Francés shall start to liquidate the proceeds corresponding to each of the minority shareholders who are registered in the relevant list delivered, upon their request. Such proceeds shall result from multiplying the number of shares by the Price plus any interest accrued thereon as from the date on which the deposit was made in the Account up to the effective date of withdrawal, with charges upon said Account.

c) The liquidation of the Transaction shall vary according to the time in which the minority shareholder demands collection of such amount corresponding to the price for its shares and according to the place where such shares are deposited:

1. If a minority shareholder wishes to collect the price before the registration of the transfer of all remaining shares held by minority shareholders for the benefit of the controlling shareholder, with Caja de Valores SA (“CVSA”):

i. If the shares to be collected have already been deposited in CVSA’s collective deposit, the depository bank and BBVA Banco Francés shall coordinate the transfer of such shares in particular for the benefit of TESA, and the minority shareholder shall collect the price through its depository bank; or

ii. If the shares to be collected have already been registered with CVSA, the latter acting as book-entry registrar, CVSA and BBVA Banco Francés shall coordinate the transfer of such shares in particular for the benefit of TESA, and the minority shareholder shall collect the price through CVSA.

In both procedures, BBVA Banco Francés shall receive a copy of the acceptance of the price by the depository bank, CVSA or the minority shareholder, as well as the documents required by the Resolution of the CNV and the regulations established by the CVSA (collectively referred to as the “Regulations Applicable to the Liquidation”), if different.

2. If a minority shareholder wishes to receive the funds after the registration of the transfer of all remaining shares held by the minority shareholders for the benefit of the controlling shareholder for CVSA but before the expiration of the 90-day period in which it may object to the price:

i. If the shares to be collected have already been deposited in CVSA’s collective deposit, the minority shareholder shall express his acceptance to CVSA through its depository bank.

ii. If the shares to be collected have already been registered with CVSA, the latter acting as book-entry registrar, the minority shareholder shall express its acceptance directly through CVSA.

CVSA, by virtue of all the acceptances received, shall from time to time, request remittance of the funds from the Escrow Agent, who shall send to CVSA the amounts corresponding to the minority shareholder, either directly or through its depository.

3. Upon the expiration of the 90-day period to object to the price, BBVA Banco Francés shall send to CVSA the funds corresponding to all outstanding shareholders who have not objected to the price, so that CVSA pays the amounts corresponding to the minority shareholders.

i. If the shares to be collected have already been deposited in CVSA’s collective deposit, through its relevant depository banks; or

ii. If the shares to be collected have already been registered in CVSA, the latter acting as book-entry registrar, directly through CVSA. TESA shall provide information, in due time and manner, to the Escrow Agent on the minority shareholders who have commenced the price objection process, for BBVA Banco Francés to send to CVSA, the payments referred to in this paragraph 3.

4. For purposes of collection by the minority shareholders, during the period set for in subparagraph 1 hereof, the Escrow Agent shall only acknowledge them as such if it has previously received the shares corresponding to such shareholder included in the list of minority shareholders delivered by TESA to BBVA Banco Francés on the date of the deposit of the funds or, should the shareholder not be included in such list, the Escrow Agent shall acknowledge them as such upon verification of their capacity as shareholders with CVSA.

For purposes of collection by the minority shareholders, during the periods set forth in paragraphs 2. and 3 hereof, the Escrow Agent shall only acknowledge them as such if they are included in the list of minority shareholders provided to the Escrow Agent by TESA upon TASA’s filing with CVSA the Declaration of Acquisition duly recorded as a public deed.

5. For purposes of implementing the transfer and control of the shares under the Tender exclusively during the period established in paragraph 1, BBVA Banco Francés in its capacity as Escrow Agent shall proceed to:

i. Open an escrow account in the collective deposit of Caja de Valores, for the exclusive purposes of the Transaction on the account and order of BBVA Banco Francés (who shall act in accordance with the provisions hereof), under the name of TELEFÓNICA S.A.- ADQUISICIÓN RESIDUAL ACCIONES TELEFÓNICA ARGENTINA S.A. — ORDEN BBVA BANCO FRANCÉS S.A. TELEFÓNICA S.A.- ACQUISITION OF REMAINING CAPITAL STOCK IN TELEFÓNICA ARGENTINA S.A. — TO THE ORDER OF BBVA BANCO FRANCÉS S.A. (the “Collective Escrow Account”) in which all shares acquired under the Tender from those shareholders who have deposited them in the collective deposit of CVSA’s collective deposit, shall be deposited; and

ii. Open an escrow account in the book-entry register of Caja de Valores for the exclusive purposes of the Transaction on the account and order of BBVA Banco Francés (who shall act in accordance with the provisions hereof), under the name of TELEFÓNICA S.A.- ADQUISICIÓN RESIDUAL ACCIONES TELEFÓNICA ARGENTINA S.A. — ORDEN BBVA BANCO FRANCÉS S.A. TELEFÓNICA S.A.- ACQUISITION OF REMAINING CAPITAL STOCK IN TELEFÓNICA ARGENTINA S.A. — TO THE ORDER OF BBVA BANCO FRANCÉS S.A. (the “Registration Escrow Account “), in which all shares acquired under the Tender from those shareholders who have deposited them directly in the book-entry register of CVSA, shall be deposited;

Simultaneously with the filing of the copy of the public deed of the Declaration of Acquisition in CVSA, TESA shall request CVSA the transfer of all shares acquired and deposited in the accounts described in paragraphs i and ii, to an account in the name of TESA in the Book-Entry Register in CVSA.

d) Deal with any inquiry made by TASA’s minority shareholders, either directly or through its custodians, only with regard to the manner in which the liquidation of the Transaction is carried out. e) provide information to TESA with regard to the liquidated transactions, on a weekly basis, during the first ninety (90) days from the date of the initial deposit in the Account; and, on a monthly basis as from the expiration of said period. The detailed list of the minority shareholders submitted and the number of relevant shares held by each of them shall be informed to the extent that CVSA provides such information to the Escrow Agent, information that BBVA Banco Francés shall request at least once at the end of each month from CVSA.

3. Representations and Commitments

(a) Representations: BBVA Banco Francés and TESA acknowledge that the representations made below are true and accurate as of this date, and that they shall continue as such so long as this Proposal is accepted and remains in force:

(i) That both BBVA Banco Francés and TESA are corporations duly incorporated and in good standing in accordance with the laws of the jurisdiction of their organization, incorporation or creation.

(ii) That TESA’s representative executing this Proposal, has the power to do so it and to execute any other document related hereto, as well as to submit any other document that may be requested as a consequence hereof, or to carry out and perform all obligations arising herefrom.

(iii) That both TESA and BBVA Banco Francés have taken all necessary measures to authorize the execution and performance of this Proposal.

(iv) That the execution and performance of this Proposal do not violate or conflict with (a) any law, regulation, judicial, arbitral or administrative resolution or of any nature whatsoever applicable to the Acquisition, TESA and/or Banco Francés; (b) the bylaws of BBVA Banco Francés or TESA; and (c) any other contractual restriction applicable to TESA, or BBVA Banco Francés.

(v) That the obligations assumed under this agreement are legal, valid and enforceable under the terms and conditions hereof.

(vi) That TESA is responsible for obtaining all necessary approvals concerning the Acquisition from the CNV and the Buenos Aires Stock Exchange; such approvals shall be duly notified to the Escrow Agent. Notwithstanding the foregoing, the Escrow Agent shall cooperate with TESA in the obtaining of such approvals whenever information on the Escrow Agent is required.

(vii) That the Account complies with all the requirements established by the Argentine Laws in general and with those provisions set forth in Section 28 of the Executive Order, in particular.

(b) Commitments:

(i) As of the date of this Proposal there are legal, financial, accounting and exchange issues pending to be defined; therefore, BBVA Banco Francés and TESA agree to make their best efforts to provide its assistance in the successful completion of the Transaction, all of the above in compliance with the appointment established in the first paragraph, and provided always that it does

not imply, for BBVA Banco Francés and/or TESA, a violation or breach of any local or foreign law or regulation whatsoever.

(ii) TESA shall make available to the Escrow Agent any information that is reasonably required by the Escrow Agent to perform all the tasks inherent in such capacity.

Any and all notices or communications made, either by means of newspapers and/or notices to shareholders, where the Escrow Agent is mentioned for any reason whatsoever, whether for its performance as Escrow Agent or for the procedure to collect the offered consideration by the minority shareholders, shall be made with the Escrow Agent’s prior consent, which shall not be delayed or denied without reasonable cause.

4. Liability

TESA acknowledges that BBVA Banco Francés shall not assume any liability beyond that which is established in this Proposal.

Furthermore, it is hereby stated that the obligations herein assumed by BBVA Banco Francés (if accepted) shall under no circumstances guarantee the results of the Tender.

It is hereby established that in accordance with the procedure set forth in Communication No. 3846 by CVSA, BBVA Banco Francés, in its capacity as Escrow Agent for the Tender shall be the party liable to make all payments to CVSA. Therefore, upon performance of all the mentioned payments to CVSA under Section 2, subsection c), paragraphs 2. and 3. hereof, BBVA Banco Francés is released from any liability related to the same, except for any misconduct or gross negligence.

5. Confidentiality

TESA and BBVA Banco Francés are hereby bound not to disclose or inform to third parties, other than TASA, without the prior written consent of the other party, the content of this Proposal and the content of the information mutually furnished by them derived herefrom, except to the extent that the same is required by law or competent authority.

Any information or document that TESA delivers to BBVA Banco Francés concerning the Acquisition and this Tender shall be confidential. BBVA Banco Francés is hereby bound to keep strict confidentiality of said information and not to use it for any purposes other than those for which it was provided. This confidentiality obligation shall not apply to: (i) information that is accessible to

the public in general other than by the breach of this confidentiality obligation by BBVA Banco Francés, which has been published prior to the date of this Proposal, has been received by third parties without restrictions and without implying a breach of this Proposal or which has been independently developed by BBVA Banco Francés; (ii) in the event of a judicial or administrative order and provided always that the party who has received the relevant order, previously notifies the other in writing, the obligation to disclose such information and delivers solely to such judicial or administrative body the information so requested.

Upon termination of this Proposal, if accepted, the parties agree that they shall continue to be bound by the confidentiality obligations notwithstanding the termination of the remaining obligations by performance thereof

6. Indemnity

TESA shall indemnify and hold BBVA Banco Francés harmless to the extent established below, whether the Acquisition is carried out or temporarily suspended or permanently cancelled. BBVA Banco Francés, its officers, director or employees, agents and/or related companies (any of such Persons, an “Indemnifiable Person”) shall receive compensation and be held harmless by TESA in an unconditional, total and irrevocable manner against any injury (including commissions, fees and reasonable costs duly evidenced) that said Indemnifiable Person may suffer and which is caused by TESA’s acts as a consequence and by reason of: (i) failure to provide in due time an manner, the information or documents necessary for the performance of this Proposal by BBVA Banco Francés; (ii) the existence of any mistake, omission or falsehood in the information provided referred to in the previous subsection, and which has an adverse material effect and that may be attributable to TESA; (iii) any claim for principal, compensatory interest, default interest, and/or fines or any other penalties determined, or imposed by any governmental authority during the course of the statute of limitations that may be applicable concerning the determination or application of any tax affecting this Proposal, except for those that correspond to the Escrow Agent, as the case may be, (iv) any other injury, loss, expense or claim that BBVA Banco Francés may suffer, under the Acquisition, or by the application of Argentine and/or foreign laws or regulations in its capacity as Escrow Agent. TESA shall be bound to hold any Indemnifiable Person harmless in any of the above cases (i), (ii) (iii) and (iv), except for misconduct or gross negligence by the Indemnifiable Person.

7. Term:

This Proposal, if accepted, shall be effective (i) until all the minority shareholders that are included in the list mentioned in Section 2 (a) hereof, have

received the deposit of the monetary proceeds to which they are entitled, in accordance with the provisions set forth in Section 2, from CVSA or (ii) until the Early Termination, whichever occurs first.

8. Early Termination

This proposal, if accepted, shall be early terminated due to: (i) any changes in the legislation that render the performance hereof illegal or impossible or due to any other circumstance not attributable to BBVA Banco Francés that renders the performance hereof impossible (including any judicial order) and (ii) at TESA’s sole discretion. For the latter case, compensation to be paid by TESA shall be 50% (fifty per cent) of the fixed fees established in Section 9 in the event that the cancellation is made before making the deposit of the funds agreed upon, and it shall be 100% in the event that the funds are deposited for the benefit of the minority shareholders.

In the event of Early Termination, TESA shall reimburse BBVA Banco Francés for all reasonable and duly evidenced expenses and costs that have been incurred in the development of the services rendered in this Proposal, without entitling BBVA Banco Francés to receive other fees than the ones already received up to that moment.

9. Consideration for the Services

The consideration to be paid for the services rendered by BBVA Banco Francés in its capacity as Escrow Agent shall be a fixed fee of €33,300 (thirty-three thousand Euros) plus VAT, which shall be payable as follows, €16,650 plus VAT within 5 days of the acceptance of the Tender, and €16,650 plus VAT upon the deposit of the funds corresponding to the Price of the shares subject to the acquisition.

Expenses incurred in publications, correspondence, printings, taxes of any nature whatsoever- including taxes on financial transactions- and other expenses that are reasonably required for the transaction shall be borne by TESA and paid to BBVA Banco Francés within five days upon the latter’s request after being previously approved and justified by TESA.

10. Taxes

All payments to be made by TESA to BBVA Banco Francés shall be made without any deduction or withholding due to rates, taxes, contributions and/or encumbrances that result applicable at present or that may result applicable during the performance of the Transaction in the Argentine Republic. TESA accepts to afford and to pay any present or future rates, taxes, contributions

and/or encumbrances applicable on the implementation and/or execution of this and/or any other agreement or document that shall be executed in relation to the transactions herein contemplated, including, but not limited to, the Value Added Tax (VAT). Notwithstanding the foregoing, expenses due to income, net income taxes or any other taxes upon its activities and that are inherent in the activities and businesses carried out by BBVA Banco Francés shall be borne by BBVA Banco Francés.

11 Applicable Law and Jurisdiction

This Proposal, if accepted, shall be governed and construed in accordance with the laws of the Argentine Republic, and the Parties hereby agree to irrevocably submit to the jurisdiction of the Ordinary Courts of Commercial Matters of the City of Buenos Aires, any course of action or procedure arising out of or related to this Proposal and to the transactions herein mentioned.

12, Domiciles.

For purposes hereof, the domiciles of the parties shall be the following:

To: Telefónica S.A

Att: General Secretary’s Office

Distrito C. Edificio Central
Ronda de la Comunicación s/n,
28050 Madrid, ESPAÑA.

To: BBVA Banco Francés S.A.:
Att.: Ignacio Laura
Reconquista 199, Piso 1
1003 Buenos Aires, Argentina
Tel. No. (5411) 4346 4311
Fax (5411) 4646 4347
e- mail: ignacio.laura@bancofrances.com.ar

13. Miscellaneous

Any amendment to this Proposal, if accepted, shall be evidenced in a written document that expressly mentions this Proposal.

It is hereby agreed that the nullity or invalidity of any of the provisions contained herein shall not affect the validity of any other provisions contained in this Proposal.

Any change in the domiciles set forth in the section above shall only be effective once written notice thereof is given to the other party with acknowledgment of receipt. Any notice sent to such domiciles shall be valid and enforceable against the notified party.

Any failure to exercise any right herein granted to any of the parties, or any delay in the exercise of the same, shall not be construed as a waiver of such right. Likewise, the partial exercise of any other right shall not bar the complete exercise thereof or of any other right.

Any waiver by the parties to any of the terms and conditions hereof, and any consent given so that the other party may proceed in a manner other than the one contemplated herein, shall be made in writing in order to be effective. Any of such waivers or consents shall only be valid as regards the case and the purpose for which they were granted.

This proposal represents the entire agreement and understanding of the parties and supersedes any and all prior agreements, contracts and covenants, oral or written, related to the subjects referred to in this Proposal.

Should the terms and conditions of this Proposal be satisfactory to you, kindly deposit the sum of $50 (fifty) pesos in the checking account held by Francés Valores Sociedad de Bolsa S.A. 493-20-160/3 which is opened in the BBVA Banco Francés, before August 11, 2009 as advance fees for expenses, which shall be considered as a partial performance of this agreement. In the event such amount is not credited to the account before the indicated date, this Proposal shall be null and void.

Ignacio Laura — Banca de Inversión
Javier J. Daud — Manager — Banca Corporativa Europa

BBVA Banco Francés S.A.
Reconquista 199, 1er piso
Ciudad de Buenos Aires Argentina