If you are the custodial parent for IRS purposes, then you may claim then Dependent Care Expense credit and the Earned Income Tax Credit. Generally, the custodial parent is the parent with whom the child lived for the longer period of time during the year.
If you each have the child for an exactly equal amount of time, then the Tiebreaker Rule comes into effect. The custodial parent is the one with the higher adjusted gross income.
The IRS is unconcerned with what your divorce decree says about custody, it will always look first to the number of days the child stays with each parent.
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