If your rights as a parent are terminated, then your obligation to pay current / prospective support is also terminated. However, arrearage is not eliminated unless the other parent agrees to waive it or reach another agreement with you on the same, which would then have to be ratified by the Court.
That's a difficult question to answer without more information. You can't just terminate your parental rights and thereby eliminate your support obligations. If someone manages to get an order terminating your rights (and obligations) as a parent, usually the custodial parent would do this, then you won't have to pay ongoing support. You might still be responsible for past due support, especially if the money owed is for welfare payments to the other parent. You need to provide more information.
You don't have to pay child support going forward. It should be part of the termination proceeding that your child support obligation terminate. You probably will have to pay back child support, however.
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