No. Giving up your rights to see the children does not relive you of your obligation to financially care for the children. You would need another person to adopt your children and take over your role or you would need to get custody of the children to stop the support obligation.
The only way your support obligation "goes away" is if the other parent arranges an adoption, (either by a stepparent or by unrelated persons) you consent to the adoption, and the adoption is completed. After that date, your obligation to pay further support would terminate.
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