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Assuming a minor child under age 18 and the child lives with the mother and not you.

For him to claim an unrelated child *all* of the following conditions must be met:

1) He must have lived with the child the entire tax year - all 365 days except for temporary absences.
2) The parent that lived with the child must not be required to file a tax return.
3) He must have provided *more* than half of the child's total support for the tax year.   That includes rent, food and other support items.

If all 3 are not true then he cannot claim the child.

For a parent to claim, support is not an issue, but if you did not live with the child more than 1/2 the year then you would need a signed 8332 form from the mother for you to claim.  Then you could claim the exemption and child tax credit but not the EIC or child care.
**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.**