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You stated that "Note in particular that the non-custodial parent can never claim the Earned Income Credit, Head of Household filing status or the day care credit, based on that child, even when the custodial parent has released the exemption to him."  This contradicts the instructions on Form 8332, which states "It is used so the noncustodial parent can claim the child tax credit, the additional child tax credit and the credit for other dependents (if applicable)."  Also, the EIC can still be claimed by the noncustodial spouse.  The amount of EIC will depend on income and family size, but the EIC is still available for someone that has no dependents.  It is called the "childness EIC."