1. Assuming you're still unmarried, you can still file as HOH - if you paid for more than half the cost of keeping up a home for yourself and your dependent child who lived with you more than 6 months. This is true even if you sign over the right to claim the child as a dependent by using Form 8332.
2. Assuming your ex-husband is not remarried, and assuming that he does not provide a home for another child of his own, he would file as Single. He cannot file as HOH based on your custodial child.
3. As the custodial parent, you can still claim the EITC even though you have released your right to claim the child as a dependent.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
