My kids' father recently tried to give up his parental rights and was told that he could not do anything because we live in different states (he lives in Arizona and we live in California). He said I would have to file the paperwork to relinquish his rights and mentioned something about my boyfriend adopting the kids. My boyfriend is on board with the idea but we are not married. I want to know if he could adopt the kids or if the biological father can give up his rights without them being adopted.

California may allow the adoption if you can prove a long term relationship, Most courts prefer married and married for at least one year

my boyfriend adopting the kids. My boyfriend is on board with the idea but we are not married
If your boyfriend adopted your kids and you two broke up, he, unrelated to the kids, could take your kids away from you. That's why most states insist you be married for a year, to establish a solid family relationship.

Could their father give up his rights without them being adopted?

I don't think so. An expert here will confirm that.

Could their father give up his rights without them being adopted??

Nope. There are thousands of threads here asking the same question, including a sticky note at the top that deals specifically with this issue.

Could their father give up his rights without them being adopted??

Not in most states.

But he shouldn't assume, even if it were possible, that TPR would be the same thing as not having to pay child support. It isn't necessarily so.