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As long as the title to the home is in your parents' names, they are the ones who will have to pay the capital gains tax on the sale of this home, regardless of who actually made the mortgage payments.
Once the home is sold, your parents can gift you the money received from the sale. No gift tax would actually be due on the transaction since they are each allowed to give gifts in their lifetime of up to $1 million before they start paying gift tax. But since the value of the gift will exceed the allowed annual exclusion of $13,000, they would be required to file Form 709 with the IRS to report the value of the gift they are giving to you.
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