What is the procedure to follow for claiming children on taxes when no custody(Cont')?

The parent the children spend more nights with gets the claim. Sounds like this is their dad. He should file his return by mail claiming them. The IRS will send them each a letter saying that someone else claimed the same dependent, and if they aren't the person with the legal claim, they need to amend their return. Then if nobody does, the IRS will ask for proof they can claim the kids, and make the call.