You need to consult a lawyer. However, the general rule is that the father and mother each file financial statements (you can find the automated forms online and get a good estimate of what child support will look like). The law contains a formula, for ease of understanding, I'll simplify. Basically, you take the amount of time each parent has physical custody of the kids, the statute provides the child support amount, you compare the parents' incomes, and when you put it all together the non-custodial parent usually ends up paying the parent who has the kids most of the time.
A father can't "sign over his rights" to get out of child support. However, if the children are later adopted by a step parent, then that usually stops child support obligations.
Some attorneys sell unbundled legal services where you pay for just what you need and can afford. For example, some attorneys will give you an hour or two at a set price to review your lease and give you advice based on the law, prepare letters for you to sign, or sell the paperwork for the court filings; then you can proceed on your own, but knowing that your paperwork is correct.
Good luck. jim
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It is possible for a father to relinquish parental rights. If this is done, he will be off the hook for child support. It will be almost impossible for him to do this without your consent and cooperation, however. You should think about whether your children should be deprived of the support before you agree to a plan like that. Without your active cooperation the divorce court will certainly impose and allow you to enforce an obligation for the father to support his children.
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