You and your ex cannot both file Head of Household. Only a parent that has a child more than 51% of the year can file as Head of Household because the requirement for that filing status is to pay more than half of your total household expenses and must have maintained your household for your qualifying child during that time.
If 50/50 custody was maintained, neither parent would qualify as Head of Household.
In regards to the Earned Income Credit, if the child lived with each parent for the same amount of time: The parent with the higher adjusted gross income (AGI) for the year may claim the child.
If you can’t claim the qualifying child because of the tiebreaker rules, you may be eligible to claim the EITC with no qualifying child.
Qualifying Child Rules
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