What happens when both parents who are divorced claim a dependent on their tax return?

What normally will happen is that if both divorced parents try to claim a child, the IRS will flag both tax returns. They will then ask both parties to document how much time the child spent with each parent.  If  the final divorce decree allows the parent paying child support to claim the child, then that parent needs to get the other parent to sign an IRS form allowing them to claim the child on taxes.