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No.   Only the custodial parent can claim the child as a dependent.   If that parent signs a form 8332 that allows you to claim the child on your tax return you can get ONLY the child tax credit.   You cannot file as head of household, get earned income credit or the childcare credit by claiming that child.  And again---you only get the child tax credit if there is a signed 8332 --signed by the other parent.

 

There is no place on a tax return to enter child support you paid or plane fare you paid for.   Those are not deductible.

 

 

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