Can a non-custodial parent claim child on taxes?
This usually is set up as part of the divorce decree.
The default is that the custodial parent gets to claim the dependent, but it can be set up differently via the divorce decree.
In my case, I (non-custodial parent) claimed my son as a dependent for the first five years; his mother claimed him thereafter.
Each year that I claimed my son as a dependent when filing my US Federal Income Tax I obtained a signed IRS form 8332 from my ex-wife, which effectively assigned the right to claim him as a dependent to me for that tax year.