The only "custody" that the tax law cares about is physical custody - which parent the child(ren) lived with at least 1/2 (or greater part) of the tax year. For tax purposes that parent is the custodial parent. The other (non-custodial) parent can only claim if the custodial parent releases the exemption with a signed 8332 form.
Only if you have a legally enforceable written custody agreement that allows him to claim the child(ren) reguardless of the circumstances, might he be able to force you to release the exemption (dependent) to him with a 8332 form, but he would have to pursue that in a local family law court - the IRS will not get involved in local custody agreement disputes.
**Disclaimer: This post is for discussion purposes only and is NOT tax advice. The author takes no responsibility for the accuracy of any information in this post.**
