Perhaps I can rephrase your question.
How can you escape New York's sardonic age of majority (21) and statutory college support requirement?
That's a tough one. Nevada has no statute that compels paying for a child's college education absent an agreement of the parents, and their age of majority is 18. I am certain many New Yorkers would love to have their files transferred to Nevada. However, I do not believe a New York Support Magistrate will allow such a switch because he will cause New York state to lose matching funds that in these tough economic times are critical for the state.
As for your situation, as long as you stay in New York you are subject to the jurisdiction of the county family court. You would have to move to Nevada and await service of a New York petition and then move to dismiss for improper venue or move to transfer venue. You'll need a competent attorney to meet the statutory transfer requirements. However, I do not believe you'll be free of New York.
Good luck in any event.