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In USA, what circumstances (if any) make it illegal for a homeless person to “rent” an address?
It depends on the rules in the specific places you stay.  Specific places being countries or states.   Some states may consider pension payments to be taxable income, others may not.  Some may consider presence for X days to constitute residency, X days may be 60 days in a calendar year whether or not those days are continuous.   It doesn't matter so much where your mailbox or mail handling service is located, it matters: You may owe taxes in more than one place.  Some states will allow you to offset other states' taxes against theirs.  Some states in the US are really harsh on income taxes.  It's my understanding that if you own real estate in New York, all of your income, no matter the source, is taxable income in New York whether or not you were ever in the state that year. Ultimately, you can't just put up your hand and say, "that's my tax domicile so I'm exempt from all your taxes."  There is no umbrella US regulation on this topic, the states determine who they consider to be residents and how those residents are to be taxed. While it's possible you may be considered a resident of multiple states and owe income taxes in multiple states, it's equally possible that you won't meet the residency criteria for any state regardless of whether or not that state has an income tax.  The issue you face, as addressed in @Jay's answer, Oklahoma will consider you a resident of OK until you have established residency somewhere else.