As of 2012, you can give up to $13,000 per child a year without incurring a reporting obligation.
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The short answer to the question is "as much as you like." The IRS sets no cap on the total amount of money you can give your child each year. However, there are tax consequences for gifts over a certain amount, and the IRS imposes a lifetime $5.12 million gift tax exemption as well.
Gift Taxes and Estate Taxes
As of 2012, the IRS imposes a 35 percent estate tax on any estates worth over $5 million when the owner dies. To prevent wealthy individuals from circumventing the estate tax by giving their money away before they die, the IRS also imposes a gift tax, with
a lifetime $5.12 million exemption. This is no accident: The gift tax and estate tax exclusions match up by design. Any amount you use of your gift tax exclusion also counts against your estate tax exclusion. You don't get to give away $5.12 million and still qualify for the $5 million estate tax exclusion. For example, if you give away $2 million in gifts to your children while you're alive, $3 million of your estate will be eligible for the estate tax exclusion.
Gift taxes are paid by the giver, not by the recipient. The giver must track gift payments over a lifetime. The maximum gift tax rate is 35 percent -- again, the same as the estate tax rate imposed on estates greater than $5.12 million, as of 2012.
Annual Gift Tax Exemption