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As far as income tax, gifts have no effect. Gifts of any amount are not taxable to the receiver nor deductible to the giver.
However, there is a totally separate tax called the gift tax. If you gift more than $13,000 per person per year, then you would need to file a gift tax return. Filing the return doesn't necessarily mean you would owe tax because you have a lifetime gift and estate tax exemption that is currently set at 5 million dollars.
If your gift is $13,000 or less, there is no need to report anything as gift tax or income tax.