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Thank you for your question.
What you can claim and who claims what when the absent parent is able to claim dependents is a common question for divorced and seperated parents.
Since you are the custodial parent, your children are your qualifying children for the following benefits:
1. Filing head of household if you are not remarried.
2. Claiming the Earned Income Tax Credit.
3. Child care credits.
He can take only the exemption and the child tax credit.