The court will give the signed 8332 to the non-custodial parent. The non-custodial parent will claim the dependents and include that 8332 with the tax return they file.
Now if the custodial parent claimed the dependents for a tax year that is clearly indicated on the 8332 for the non-custodial parent and their tax return has already been accepted by the IRS, then the non-custodial parent has no choice other than to print, sign and mail the return to the IRS, including the 8332 with it (or a copy of it). When the IRS gets it, then the non-custodial parent will be allowed to claim the dependents and the custodial parent will have to pay some of their refund back, along with some hefty fines and penalties for filing a fraudulent return.
