You cannot claim the children on your return unless the other parent signs a form 8332 that allows you to get the $500 credit for a dependent and child tax credit. If your ex does not sign such a form you do not put those children on your return at all. Even with the signed 8332, the custodial parent is the only one who can get earned income credit or childcare credit. Without a signed 8332, the custodial parent gets all of the child-related credits.
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