In the US all your biological children still in your legal custody and any legally adopted or other legally dependant children - if no one else claims them. If you are divorced you can only claim if you are the legal custodial parent and if separated and filing separate from your spouse you have to come to an ageement on who claims the kids.
my kids mother and I not together anymore but I support my girls 365 days out a year. she have three more kids that's not my kids but her son I rise like he my son. Years around. so every year when tax time she tell me I can claims one of my girls ok cool. so when my paper work comes in the mail and then I ask for my daughter SSI card she tells me she already had file. putting all five kids on her taxes... this is the three year she did this to me. I still owe the IRS money for last year. what can I do