How does giving up parental rights work now and past

If you had read the Read First sticky on this issue at the top of the forum or any of the thousands of similar questions, you would know it DOESN'T work.

You can NOT give up your parental rights. Only a court can terminate parental rights and they will generally NOT do so except to clear the way for an adoption or if the parent represents a danger to the child.

Pretty sure it didn't work in the past either.

Was trying to make it short
Adopted two kids and found out today that the paternal parent is recieveing child support my understanding is you give up all your rights past and present

So you adopted two children! As the stepfather or what? And you found out the bio father is still receiving support payments? From who?

Stop trying to make it short and gives us the full details so we can help you.

Adopted two children
Both paternal parents gave up all parental rights and found out the paternal mother is recieveing child support from the paternal father heard that it was for back support
My understanding is you give up your rights then you give up all

Back support is not automatically erased when the child is adopted.

Again, stop trying to make it short, but Steve is correct, an Adoption does not affect support arrears. If the bio father owed back support, then he still has to pay that to the custodial parent until the arrears are made up.