Yes, it's 20 years, but the problem is that the statute of limitations extends to each period of time you violated. In other words, you MAY be able to avoid 3 years worth of arrears (unless there were subsequent orders or judgments), but not the remainder of the arrears. It's probably best that you seek to cut a deal.
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It's twenty years for orders of support entered after August, 1986. However, your violation keeps advancing so the number of years never drops.
Remember the mother holds the power to waive support, not the court. A deal cut with her is the only way to avoid a $40K arrearage, but why would she take less?
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