There is no support requirement for a parent to claim a qualifying child dependent so he doesn't need it. The only requirement is that the child not provide more than half their own support.
If you are the custodial parent who the child lived with more than half the nights of the year, you are the one who decides who can claim the child as a dependent. If you agree to let the other parent claim the child, the only thing the other parent can claim is the dependency and the child tax credit. You as the custodial parent are the one who can claim Head of Household filing status, EIC and child care credit.
