The IRS cares about where the children actually lived. Whoever had them for the most nights is the custodial parent who can claim the children as dependents. If there is a signed form 8332 then the custodial parent---the one who had them for at least 183 nights---can still get earned income credit and the childcare credit. If there is no signed agreement, then start counting up all the nights. The non-custodial parent can get the child tax credit.
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