You have it mostly right. If you sign Form 8332 your ex can get the child tax credit up until the child turns 17 (not 13).
As the custodial parent, you can still get childcare credit for a child under 13 if you pay for childcare so you can work. And if your income is within the amounts for EIC you are the only parent who can get earned income credit. He cannot claim anything for paying child support, nor are there any deductions (for either of you) for tutoring, after school activities, etc.
There are no personal exemptions any more, so that is moot. The exemption was "sort of" replaced by a $500 credit for dependents. He would get that.
As far as the IRS is concerned it is the custodial parent who gets all of the child-related credits, unless you sign 8332. Good luck--hope you prevail in court.
**Disclaimer: Every effort has been made to offer the most correct information possible. The poster disclaims any legal responsibility for the accuracy of the information that is contained in this post.**
