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Who does the child live with?    Only the parent where the child physically lived more than  half the year can claim the EIC, Child Care Credit And HOH reguardless of which spouse claims the dependent and Child tax credit.   

The  EIC, Child Care Credit And HOH can never be claimed by the parent that did not live with the child.   That is the purpose of the custody agreement questions in the dependent interview.
**Disclaimer: This post is for discussion purposes only and is NOT tax advice. The author takes no responsibility for the accuracy of any information in this post.**