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if you go through the formality of divorce, some people don't, the court could award you the right to claim the children for tax purposes even though you don't have custody.  The IRS will recognize this only if the custodial parent provides the noncustodial parent with form 8332.  this form must be signed and dated by the custodial parent and the noncustodial parent must attach the form to their tax return every year to claim the children. 

mention this to your divorce attorney because sometimes the ex refuses to comply with the court order. the IRS won't care. no 8332 you lose.