IRC§152(e) clarified the meaning of custody for dependency purposes. As usual this is not always a good thing; in general typically a custodial parent can sign a written release for the noncustodial parent may claim the child.
Now if the child is (court) emancipated or an adult (18 or older) they are treated as not being in the custody of either parent. So there is no ability for either to sign a release for the other to claim the exemption.
Now things get interesting, you have the support tests and the residency tests that need to be pasted for claiming the exemption. The education credits and deductions are also tied into these tests as well. The issue of divorce gets further complicated.
Obviously for further information please contact our office.