This is from publication 596

Example 10—Unmarried parents.

You, your 5-year-old son, and your son's father lived together all year. You and your son's father aren't married. Your son is a qualifying child of both you and his father because he meets the relationship, age, residency, and joint return tests for both you and his father. Your earned income and AGI are $12,000, and your son's father's earned income and AGI are $14,000. Neither of you had any other income. Your son's father agrees to let you treat the child as a qualifying child. This means if your son's father doesn't claim your son as a qualifying child for the EIC or any of the other tax benefits listed earlier, you can claim him as a qualifying child for the EIC and any of the other tax benefits listed earlier for which you qualify.

Example 11—Unmarried parents claim same child.

The facts are the same as in Example 10 except that you and your son's father both claim your son as a qualifying child. In this case, only your son's father will be allowed to treat your son as a qualifying child. This is because his AGI, $14,000, is more than your AGI, $12,000. You can claim the EIC without a qualifying child.