I don't think you can and I don't think you should. The reason I don't think you can is courts are generally reluctant to terminate a parent's rights. Mostly because they want to ensure the child support continues and if the parent's rights are terminated so other responsibilities such as paying child support.The reason I don't think you should is, aside from the fact that you will terminate your right to receive child support, you may sparking interest in parenting time from the other parent once he/she get a copy of the paperwork.  A court will entertain that application to try to stagger it and add counseling to help the children transition. So, if you do not want the other parent involved, I would not file anything.