The IRS will allow the dependent to the custodial parent no matter what the divorce agreement says. The agreement is a local legal document, and you could consider departing from it if you both agree and will not be going back to court over this.
This year, if the custodial parent is not claiming the dependent, they can claim the Child Care Credit, the Earned Income Credit, and the filing status Head of Household, but not the Child Tax Credit.
The noncustodial parent can only claim the Child Tax Credit in the year that he can claim the dependent, since there is no longer a personal exemption.
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