There are 5 tax benefits of a dependent (not counting college credits): dependent exemption, child tax credit, dependent care credit, qualify for head of household, qualify for earned income credit.
Only the dependent exemption and the child tax credit can be transferred to the non-custodial parent by divorce decree or release form. The other 3 benefits always and only go to the custodial parent.
As a practical matter, the IRS has no way to check unless there is a conflict. So if you and the other parent both want to pretend you were the custodial parent, you probably won't get caught. Or if your ex does not file a US tax return, and you claim the child lived with you all year, you might not get caught. But if you do get caught, you will owe the back tax, interest, and a substantial penalty for intentionally filing an inaccurate return.
