Generally speaking you do not have the right to terminate your rights to your child. A parent may in some circumstances surrender their rights to their children, but there must be someone who wishes to adopt the child in order for the court to accept your surrender and to terminate a support order. Even if the court were to accept the surrender of the parental rights, the support obligation would continue until the adoption is finalized. The Courts may also terminate your rights if you abuse or neglect your children, the child is placed in foster care and you do not fix the circumstances that make it unsafe for your child to reside with you. However even in that circumstance the support obligation of the parent would continue until the child is adopted.