If your rights are terminated, you have no ability to see the child and no responsibility to pay support. However, you can't just "ask" and have it done. In 99% of cases, your child must have a stepparent willing to adopt him or her in order for the judge to allow you to give up your rights and responsibility to support this way.
You may choose not to exercise your rights to bond with your child and have parenting time with your child, but you are still obligated to financially support that child, as it is the child's right to be supported by both parents to the extent they are each reasonably able.
If your parental rights are terminated, then you would not be responsible for child support. However, just asking for it doesn't work unless the court orders it.
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