The money you hear about people getting for just filing a tax return claiming kids requires them to have some earned income (wages or self employment). Without earned income, they are not eligible for the "refundable" Earned Income Credit or Additional Child Tax Credit. Both credits are calculated on the amount of earned income you have. No earned income means no "refund". A small amount of earned income means a small refund. The child tax credit does not "kick in" unless you have at least $2500 of earned income.
You could allow the non-custodial parent to claim the children. Non-custodial parents are allowed to claim the child tax credit, but not the Earned income credit. With 3 kids, the child tax credit is worth as much as $6000 to him.
