Oftentimes a divorce agreement would actually spell out which parent was allowed to claim the child as an exemption. Since there is no divorce agreement in this case, the IRS would typically take the stand that the custodial parent, the one the child spends most of the time with, has the right to claim the exemption. They also assume that the custodial parent is providing the majority of the support.
However, you could be entitled to take a deduction for the child, if the mother is willing to complete a Form 8332 for the IRS which releases her claim to the exemption. This form can be filed for one year only or can designate a specific period of years that the form remains in effect. If you are helping the mother with support payments, she may be willing to sign this form. But you would have to have this form in order to claim the child as an exemption, regardless of how much money the mother does or does not make.
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