<?xml version="1.0" encoding="UTF-8"?>

<!--XBRL Document Created with the Workiva Platform-->
<!--Copyright 2026 Workiva-->
<!--r:01a18863-a6fa-7e77-a0b2-85d126d0c170,g:64ee116f-b5ea-440e-92f2-b97bd2c44edf-->
<link:linkbase xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.xbrl.org/2003/linkbase http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd">
  <link:roleRef roleURI="http://xbrl.sec.gov/cef/role/N2" xlink:type="simple" xlink:href="https://xbrl.sec.gov/cef/2026/cef-2026.xsd#N2"/>
  <link:presentationLink xlink:role="http://xbrl.sec.gov/cef/role/N2" xlink:type="extended">
    <link:loc xlink:type="locator" xlink:label="loc_cef_AllRisksMember" xlink:href="https://xbrl.sec.gov/cef/2026/cef-2026.xsd#cef_AllRisksMember"/>
    <link:loc xlink:type="locator" xlink:label="loc_ck0001287032_IndebtednessCouldAdverselyAffectBusinessMember" xlink:href="ck0001287032-20261029.xsd#ck0001287032_IndebtednessCouldAdverselyAffectBusinessMember"/>
    <link:presentationArc order="1" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_cef_AllRisksMember" xlink:to="loc_ck0001287032_IndebtednessCouldAdverselyAffectBusinessMember" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/label"/>
    <link:loc xlink:type="locator" xlink:label="loc_ck0001287032_DowngradeSuspensionOrWithdrawalOfRatingByRatingAgencyMember" xlink:href="ck0001287032-20261029.xsd#ck0001287032_DowngradeSuspensionOrWithdrawalOfRatingByRatingAgencyMember"/>
    <link:presentationArc order="2" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_cef_AllRisksMember" xlink:to="loc_ck0001287032_DowngradeSuspensionOrWithdrawalOfRatingByRatingAgencyMember" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/label"/>
    <link:loc xlink:type="locator" xlink:label="loc_ck0001287032_IncreaseInMarketInterestRatesMember" xlink:href="ck0001287032-20261029.xsd#ck0001287032_IncreaseInMarketInterestRatesMember"/>
    <link:presentationArc order="3" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_cef_AllRisksMember" xlink:to="loc_ck0001287032_IncreaseInMarketInterestRatesMember" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/label"/>
    <link:loc xlink:type="locator" xlink:label="loc_ck0001287032_NotesSubordinatedToExistingAndFutureIndebtednessAndLiabilitiesOfSubsidiariesMember" xlink:href="ck0001287032-20261029.xsd#ck0001287032_NotesSubordinatedToExistingAndFutureIndebtednessAndLiabilitiesOfSubsidiariesMember"/>
    <link:presentationArc order="4" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_cef_AllRisksMember" xlink:to="loc_ck0001287032_NotesSubordinatedToExistingAndFutureIndebtednessAndLiabilitiesOfSubsidiariesMember" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/label"/>
    <link:loc xlink:type="locator" xlink:label="loc_ck0001287032_IndenturesWillContainLimitedProtectionMember" xlink:href="ck0001287032-20261029.xsd#ck0001287032_IndenturesWillContainLimitedProtectionMember"/>
    <link:presentationArc order="5" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_cef_AllRisksMember" xlink:to="loc_ck0001287032_IndenturesWillContainLimitedProtectionMember" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/label"/>
    <link:loc xlink:type="locator" xlink:label="loc_ck0001287032_UnableToRepurchaseUponChangeOfControlMember" xlink:href="ck0001287032-20261029.xsd#ck0001287032_UnableToRepurchaseUponChangeOfControlMember"/>
    <link:presentationArc order="6" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_cef_AllRisksMember" xlink:to="loc_ck0001287032_UnableToRepurchaseUponChangeOfControlMember" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/label"/>
    <link:loc xlink:type="locator" xlink:label="loc_ck0001287032_RestructuringTransactionsMayNotConstituteChangeOfControlMember" xlink:href="ck0001287032-20261029.xsd#ck0001287032_RestructuringTransactionsMayNotConstituteChangeOfControlMember"/>
    <link:presentationArc order="7" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_cef_AllRisksMember" xlink:to="loc_ck0001287032_RestructuringTransactionsMayNotConstituteChangeOfControlMember" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/label"/>
    <link:loc xlink:type="locator" xlink:label="loc_ck0001287032_ProvisionsOfTheNotesCouldDiscourageAnAcquisitionOfUsByAThirdPartyMember" xlink:href="ck0001287032-20261029.xsd#ck0001287032_ProvisionsOfTheNotesCouldDiscourageAnAcquisitionOfUsByAThirdPartyMember"/>
    <link:presentationArc order="8" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_cef_AllRisksMember" xlink:to="loc_ck0001287032_ProvisionsOfTheNotesCouldDiscourageAnAcquisitionOfUsByAThirdPartyMember" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/label"/>
    <link:loc xlink:type="locator" xlink:label="loc_ck0001287032_TradingMarketForNotesNotAssuredMember" xlink:href="ck0001287032-20261029.xsd#ck0001287032_TradingMarketForNotesNotAssuredMember"/>
    <link:presentationArc order="9" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_cef_AllRisksMember" xlink:to="loc_ck0001287032_TradingMarketForNotesNotAssuredMember" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/label"/>
    <link:loc xlink:type="locator" xlink:label="loc_ck0001287032_CorporateLevelTaxesCouldAdverselyAffectCashFlowMember" xlink:href="ck0001287032-20261029.xsd#ck0001287032_CorporateLevelTaxesCouldAdverselyAffectCashFlowMember"/>
    <link:presentationArc order="10" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_cef_AllRisksMember" xlink:to="loc_ck0001287032_CorporateLevelTaxesCouldAdverselyAffectCashFlowMember" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/label"/>
    <link:loc xlink:type="locator" xlink:label="loc_ck0001287032_MayRedeemNotesWhenInterestRatesAreLowMember" xlink:href="ck0001287032-20261029.xsd#ck0001287032_MayRedeemNotesWhenInterestRatesAreLowMember"/>
    <link:presentationArc order="11" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_cef_AllRisksMember" xlink:to="loc_ck0001287032_MayRedeemNotesWhenInterestRatesAreLowMember" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/label"/>
    <link:loc xlink:type="locator" xlink:label="loc_ck0001287032_IndentureWillContainLimitedProtectionForHoldersOfTheNotesMember" xlink:href="ck0001287032-20261029.xsd#ck0001287032_IndentureWillContainLimitedProtectionForHoldersOfTheNotesMember"/>
    <link:presentationArc order="12" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_cef_AllRisksMember" xlink:to="loc_ck0001287032_IndentureWillContainLimitedProtectionForHoldersOfTheNotesMember" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/label"/>
    <link:loc xlink:type="locator" xlink:label="loc_ck0001287032_NAVCalculationMayBeHigherOrLowerMember" xlink:href="ck0001287032-20261029.xsd#ck0001287032_NAVCalculationMayBeHigherOrLowerMember"/>
    <link:presentationArc order="13" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_cef_AllRisksMember" xlink:to="loc_ck0001287032_NAVCalculationMayBeHigherOrLowerMember" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/label"/>
    <link:loc xlink:type="locator" xlink:label="loc_ck0001287032_DeedOfTrustContainsVariousCovenantsWhichCouldAffectLiquidityMember" xlink:href="ck0001287032-20261029.xsd#ck0001287032_DeedOfTrustContainsVariousCovenantsWhichCouldAffectLiquidityMember"/>
    <link:presentationArc order="14" xlink:arcrole="http://www.xbrl.org/2003/arcrole/parent-child" xlink:from="loc_cef_AllRisksMember" xlink:to="loc_ck0001287032_DeedOfTrustContainsVariousCovenantsWhichCouldAffectLiquidityMember" xlink:type="arc" preferredLabel="http://www.xbrl.org/2003/role/label"/>
  </link:presentationLink>
</link:linkbase>
