When dealing with the IRS, what any decree or custody agreement may say does not concern the IRS. The IRS has their own rules concerning who the custodial parent is. Those rules can only be over-ridden by a federal judge. Since a federal judge does not deal with divorce, separation or custody matters I feel confident in saying that will never happen.
Basically, the custodial parent is the one with whom the child lived for 183 or more nights of the tax year. Those nights do not have to be consecutive either.
The custodial parent can allow the non-custodial parent to claim the child, if that custodial parent signs IRS Form 8332 giving the non-custodial parent the right to claim them. However, even with a signed 8332 there are certain things as outlined by other posts in this thread that the custodial parent still claims, and the non-custodial parent can not claim even with a signed 8332.
