Correct. If you two are in agreement on him claiming the children and the related credits, don't even enter them on your return.
Having custody of your child usually means you can claim that child as a dependent on your taxes. But if you don't have to file a tax return, or you reach an agreement with your child's noncustodial parent, you can let them take the child as a dependent instead with Form 8332.
The child's noncustodial parent must be eligible to claim the child(ren) as a dependent. The rules for claiming a dependent usually require the parent to live with the child for more than half the year. This rule can be waived when the parents are divorced, separated or live apart from each other.
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