<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><Version>2.4.0.8</Version><ReportLongName>22107100 - Disclosure - Distribution of Subsidiary</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column FlagID="0"><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><CurrencyCode /><FootnoteIndexer /><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName /><CurrencySymbol /><contextRef><ContextID>D2012</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0001254699</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2012-01-01T00:00:00</PeriodStartDate><PeriodEndDate>2012-12-31T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS /><CurrencyCode /><OriginalCurrencyCode /></MCU><CurrencySymbol /><Labels><Label Key="CalendarSupplement" Id="0" Label="12 Months Ended" /><Label Key="Calendar" Id="1" Label="Dec. 31, 2012" /></Labels></Column></Columns><Rows><Row FlagID="0"><Id>1</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>1</Level><ElementName>us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:stringItemType</ElementDataType><SimpleDataType>string</SimpleDataType><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Distribution of Subsidiary [Abstract]</Label></Row><Row FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>qvc_DistributionOfSubsidiaryTextBlock</ElementName><ElementPrefix>qvc_</ElementPrefix><IsBaseElement>false</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>terseLabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="D2012" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;div style="font-size:10.0pt;font-family:Times New Roman;"&gt;
&lt;div style="FONT-SIZE: 10pt; PADDING-BOTTOM: 12px; TEXT-ALIGN: justify;"&gt;&lt;font style="FONT-WEIGHT: bold; FONT-SIZE: 10pt; FONT-FAMILY: inherit;"&gt;(3) Distribution of Subsidiary&lt;/font&gt;&lt;/div&gt;
&lt;div style="FONT-SIZE: 10pt; PADDING-BOTTOM: 12px; TEXT-ALIGN: justify;"&gt;&lt;font style="FONT-SIZE: 10pt; FONT-FAMILY: inherit;"&gt;On May 6, 2010, the Company distributed 100% of its interest in one of its consolidated subsidiaries, Commerce Technologies, Inc. ("Commerce"), to Liberty. The transfer was recorded at book value and the Company recognized no gain or loss on the transaction and is included in Contribution received from (dividend paid to) Liberty and other in the consolidated statements of equity. At the time of the transfer, the net book value of Commerce consisted of the following components (in millions):&lt;/font&gt;
&lt;div style="PADDING-LEFT: 0px; TEXT-INDENT: 0px; PADDING-TOP: 10px;"&gt;
&lt;table style="text-align:left;FONT-SIZE: 10pt; WIDTH: 100%; FONT-FAMILY: Times New Roman; BORDER-COLLAPSE: collapse; TEXT-ALIGN: left;" cellspacing="0" cellpadding="0"&gt;

&lt;tr style="padding:0;"&gt;
&lt;td colspan="4"&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr style="padding:0;"&gt;
&lt;td width="88%"&gt;&lt;/td&gt;
&lt;td width="1%"&gt;&lt;/td&gt;
&lt;td width="10%"&gt;&lt;/td&gt;
&lt;td width="1%"&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr style="padding:0;"&gt;
&lt;td style="PADDING-RIGHT: 2px; BORDER-TOP: #000000 2px solid; PADDING-LEFT: 2px; PADDING-BOTTOM: 2px; VERTICAL-ALIGN: bottom; PADDING-TOP: 2px; BACKGROUND-COLOR: #cceeff;"&gt;
&lt;div style="FONT-SIZE: 10pt; TEXT-ALIGN: left;"&gt;&lt;font style="FONT-SIZE: 10pt; FONT-FAMILY: inherit;"&gt;Cash&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;
&lt;td style="BORDER-TOP: #000000 2px solid; PADDING-LEFT: 2px; PADDING-BOTTOM: 2px; VERTICAL-ALIGN: bottom; PADDING-TOP: 2px; BACKGROUND-COLOR: #cceeff;"&gt;
&lt;div style="FONT-SIZE: 10pt; TEXT-ALIGN: left;"&gt;&lt;font style="FONT-SIZE: 10pt; FONT-FAMILY: inherit;"&gt;$&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;
&lt;td style="BORDER-TOP: #000000 2px solid; PADDING-BOTTOM: 2px; VERTICAL-ALIGN: bottom; PADDING-TOP: 2px; BACKGROUND-COLOR: #cceeff;"&gt;
&lt;div style="FONT-SIZE: 10pt; TEXT-ALIGN: right;"&gt;&lt;font style="FONT-SIZE: 10pt; FONT-FAMILY: inherit;"&gt;12&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;
&lt;td style="BORDER-TOP: #000000 2px solid; VERTICAL-ALIGN: bottom; BACKGROUND-COLOR: #cceeff;"&gt;
&lt;div style="FONT-SIZE: 10pt; TEXT-ALIGN: left;"&gt;&lt;font style="FONT-SIZE: 10pt; FONT-FAMILY: inherit;"&gt;&lt;br /&gt;&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr style="padding:0;"&gt;
&lt;td style="PADDING-RIGHT: 2px; PADDING-LEFT: 2px; PADDING-BOTTOM: 2px; VERTICAL-ALIGN: bottom; PADDING-TOP: 2px;"&gt;
&lt;div style="FONT-SIZE: 10pt; TEXT-ALIGN: left;"&gt;&lt;font style="FONT-SIZE: 10pt; FONT-FAMILY: inherit;"&gt;Goodwill&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;
&lt;td style="PADDING-LEFT: 2px; PADDING-BOTTOM: 2px; VERTICAL-ALIGN: bottom; PADDING-TOP: 2px;" colspan="2"&gt;
&lt;div style="FONT-SIZE: 10pt; TEXT-ALIGN: right;"&gt;&lt;font style="FONT-SIZE: 10pt; FONT-FAMILY: inherit;"&gt;9&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;
&lt;td style="VERTICAL-ALIGN: bottom;"&gt;
&lt;div style="FONT-SIZE: 10pt; TEXT-ALIGN: left;"&gt;&lt;font style="FONT-SIZE: 10pt; FONT-FAMILY: inherit;"&gt;&lt;br /&gt;&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr style="padding:0;"&gt;
&lt;td style="PADDING-RIGHT: 2px; PADDING-LEFT: 2px; PADDING-BOTTOM: 2px; VERTICAL-ALIGN: bottom; PADDING-TOP: 2px; BACKGROUND-COLOR: #cceeff;"&gt;
&lt;div style="FONT-SIZE: 10pt; TEXT-ALIGN: left;"&gt;&lt;font style="FONT-SIZE: 10pt; FONT-FAMILY: inherit;"&gt;Other assets&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;
&lt;td style="PADDING-LEFT: 2px; PADDING-BOTTOM: 2px; VERTICAL-ALIGN: bottom; PADDING-TOP: 2px; BACKGROUND-COLOR: #cceeff;" colspan="2"&gt;
&lt;div style="FONT-SIZE: 10pt; TEXT-ALIGN: right;"&gt;&lt;font style="FONT-SIZE: 10pt; FONT-FAMILY: inherit;"&gt;10&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;
&lt;td style="VERTICAL-ALIGN: bottom; BACKGROUND-COLOR: #cceeff;"&gt;
&lt;div style="FONT-SIZE: 10pt; TEXT-ALIGN: left;"&gt;&lt;font style="FONT-SIZE: 10pt; FONT-FAMILY: inherit;"&gt;&lt;br /&gt;&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr style="padding:0;"&gt;
&lt;td style="PADDING-RIGHT: 2px; PADDING-LEFT: 2px; PADDING-BOTTOM: 2px; VERTICAL-ALIGN: bottom; PADDING-TOP: 2px;"&gt;
&lt;div style="FONT-SIZE: 10pt; TEXT-ALIGN: left;"&gt;&lt;font style="FONT-SIZE: 10pt; FONT-FAMILY: inherit;"&gt;Liabilities&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;
&lt;td style="PADDING-LEFT: 2px; PADDING-BOTTOM: 2px; VERTICAL-ALIGN: bottom; PADDING-TOP: 2px; BORDER-BOTTOM: #000000 1px solid;" colspan="2"&gt;
&lt;div style="FONT-SIZE: 10pt; TEXT-ALIGN: right;"&gt;&lt;font style="FONT-SIZE: 10pt; FONT-FAMILY: inherit;"&gt;(10&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;
&lt;td style="PADDING-RIGHT: 2px; PADDING-BOTTOM: 2px; VERTICAL-ALIGN: bottom; PADDING-TOP: 2px; BORDER-BOTTOM: #000000 1px solid;"&gt;
&lt;div style="FONT-SIZE: 10pt; TEXT-ALIGN: left;"&gt;&lt;font style="FONT-SIZE: 10pt; FONT-FAMILY: inherit;"&gt;)&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr style="padding:0;"&gt;
&lt;td style="PADDING-RIGHT: 2px; PADDING-LEFT: 20px; PADDING-BOTTOM: 2px; VERTICAL-ALIGN: bottom; PADDING-TOP: 2px; BORDER-BOTTOM: #000000 1px solid; BACKGROUND-COLOR: #cceeff;"&gt;
&lt;div style="FONT-SIZE: 10pt; TEXT-ALIGN: left;"&gt;&lt;font style="FONT-SIZE: 10pt; FONT-FAMILY: inherit;"&gt;Net book value&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;
&lt;td style="PADDING-LEFT: 2px; PADDING-BOTTOM: 2px; VERTICAL-ALIGN: bottom; PADDING-TOP: 2px; BORDER-BOTTOM: #000000 1px solid; BACKGROUND-COLOR: #cceeff;"&gt;
&lt;div style="FONT-SIZE: 10pt; TEXT-ALIGN: left;"&gt;&lt;font style="FONT-SIZE: 10pt; FONT-FAMILY: inherit;"&gt;$&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;
&lt;td style="PADDING-BOTTOM: 2px; VERTICAL-ALIGN: bottom; PADDING-TOP: 2px; BORDER-BOTTOM: #000000 1px solid; BACKGROUND-COLOR: #cceeff;"&gt;
&lt;div style="FONT-SIZE: 10pt; TEXT-ALIGN: right;"&gt;&lt;font style="FONT-SIZE: 10pt; FONT-FAMILY: inherit;"&gt;21&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;
&lt;td style="VERTICAL-ALIGN: bottom; BORDER-BOTTOM: #000000 1px solid; BACKGROUND-COLOR: #cceeff;"&gt;
&lt;div style="FONT-SIZE: 10pt; TEXT-ALIGN: left;"&gt;&lt;font style="FONT-SIZE: 10pt; FONT-FAMILY: inherit;"&gt;&lt;br /&gt;&lt;/font&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;/div&gt;&lt;/div&gt;
&lt;/div&gt;</NonNumbericText><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>nonnum:textBlockItemType</ElementDataType><SimpleDataType>na</SimpleDataType><ElementDefenition>The entire disclosure relating to the distribution of a consolidated subsidiary to the entity's parent company.</ElementDefenition><ElementReferences>No definition available.</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Distribution of Subsidiary</Label></Row></Rows><Footnotes /><IsEquityReport>false</IsEquityReport><ReportName>Distribution of Subsidiary</ReportName><MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel><SharesRoundingLevel>UnKnown</SharesRoundingLevel><PerShareRoundingLevel>UnKnown</PerShareRoundingLevel><ExchangeRateRoundingLevel>UnKnown</ExchangeRateRoundingLevel><HasCustomUnits>true</HasCustomUnits><IsEmbedReport>false</IsEmbedReport><IsMultiCurrency>false</IsMultiCurrency><ReportType>Sheet</ReportType><RoleURI>http://www.qvc.com/role/DistributionOfSubsidiary</RoleURI><NumberOfCols>1</NumberOfCols><NumberOfRows>2</NumberOfRows></InstanceReport>
