As far as taxes are concerned, if the child lived with you for more than half the year, you are the custodial parent. That means that you are entitled to claim the child as a dependent. There is no requirement in the tax law for you to give anything to your ex. However, there are obviously other considerations here besides taxes. You should consult your lawyer.
Your ex can cause you trouble when you file your tax return if she files before you and claims the child. That would prevent you from e-filing if you also claim the child. You would have to file your tax return by mail. Then the IRS will send notices to both you and your ex. The first notice will say that you should amend your tax return to not claim the child if you are not entitled to. If neither of you amends your tax return to remove the child, the next notice will ask each of you for information to prove that you are entitled to claim the child. The IRS will then determine which of you is entitled to claim the child. The one who is not entitled to claim the child will have to pay additional tax plus penalties and interest.
This answer has been verified for accuracy by an Intuit expert employee
