You need to file a petition to terminate your parental rights, though whether it is granted will be based on the "best interests" standard, and according to the provisions set forth in the applicable statutes. You may be able to file a Pauper's Affidavit to get the court fees waived. However, I would first attempt to see if a local attorney may be willing to represent you pro bono. Good luck.
Terminating your parental rights is a rather drastic and permanent measure and it is something the courts take very seriously. You should think long and hard about whether you want to do this because if your rights are terminated, it is within the father's discretion to allow you to see the children. While it is true your child support obligation would be alleviated, you will have absolutely no say in any decisions that are made for the children. You must be going through a very tough situation, but I urge you to figure out all the options you can before you consider such a step.
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