The only ways parental rights and responsibilities can be terminated are a dependency action (CPS taking your child away because you are unfit) and an adoption (someone else wanting to take over your role as parent)...otherwise, you can't just walk away from being a parent.
Custody and support are totally separate issues. the law will not force you to have a relationship with your children, but you will be expected to support them, at least until the day comes that another adult is willing to assume that obligation and raise your children.
Best wishes for an outcome you can accept, and please remember to designte a best answer.
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See my AVVO Legal Guides on child custody and modification of parenting plans. Click on my photo, scroll down to "Contribution" and click on "Legal Guides". Then you can find the topics that relate to your situation. In most cases the noncustodial parent cannot "give up" their parental rights. Parental rights can be terminated in a case of severe child abuse or neglect, or in connection with a proceeding for another person (like a step-parent) to adopt the child.
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