<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0201</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2004-02-29</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0000818762</issuerCik>
        <issuerName>3333 HOLDING CORP</issuerName>
        <issuerTradingSymbol>CTX</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001016215</rptOwnerCik>
            <rptOwnerName>LOW JOSIAH O III</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>100 CEDAR CLIFF RD</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>RIVERSIDE</rptOwnerCity>
            <rptOwnerState>CT</rptOwnerState>
            <rptOwnerZipCode>06878</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <transactionDate>
                <value>2004-02-29</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>0.0650</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.0100</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                    <footnoteId id="F2"/>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">3333 Holding Corporation formerly traded in tandem with Centex Corporation pursuant to a Nominee Agreement dated November 30, 1987 (as amended, the &quot;Nominee Agreement&quot;).  Each person who is the beneficial owner of shares of Centex Corporation common stock was also the beneficial owner of an undivided interest in 1,000 shares (&quot;Shares&quot;) of common stock of 3333 Holding Corporation, which Shares were held of record by a nominee.  Each beneficial owner's proportionate ownership of the Shares was based on the number of shares of Centex common stock that he owns divided by the total number of outstanding shares of Centex common stock.  The Nominee Agreement was terminated on February 29, 2004.</footnote>
        <footnote id="F2">The Shares were disposed of pursuant to the effectiveness of the merger described in that certain Agreement and Plan of Merger by and among Centex Corporation, 3333 Acquisition Corporation, and 3333 Holding Corporation dated November 17, 2003, which caused the cancellation of the Shares.  The .0650 shares represent fractional ownership of 3333 Holding Corporation as a result of the reporting person's ownership of 4,000 shares of common stock of Centex Corporation.  In the merger, for their interest in the Shares, stockholders received merger consideration in an amount equal to $.01 per share of Centex common stock.  The reporting person received an amount equal to $.01 per share of Centex common stock owned by the reporting person for the disposal of the reporting person's interest in the Shares.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/Josiah O. Low, III</signatureName>
        <signatureDate>2004-03-02</signatureDate>
    </ownerSignature>
</ownershipDocument>

