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Now mine looks boring compared to that one https://images.app.goo.gl/RbQrATCyqPLTQXxh9

They have to establish a state "residence" by where they vote, drivers licenses, where they get their mail, where vehicles, including the boat, are registered.

https://www.forbes.com/sites/peterjreilly/2019/08/23/what-happens-when-you-are-a-full-year-resident-of-more-than-one-state/#2f83b52b399c

But then most states will give at least some credit for tax paid - on the same income - to another state. Who gets precedence is a whole 'nother can of worms!

Most states are reluctant to give up residents until they sever all ties and "stick the landing" in a new state as residents. If the boat is sailing around, IL might try to claim they are still IL residents, that they have not established residency in a different state. Document, document, document where they are, for how long, what ties they have to each state, where are their "treasures" stored/ photos, heirlooms, etc., where do they worship/go to doctors/vote. Read the residency requirements for each state they dock in. States do not coordinate their requirements. You may find that they can be residents of two states during overlapping time periods. This can be a big deal if taxation of retirement income is an issue for them.

Each state has its own residency requirements - most range between 30 and 90 days - primarily the assessment of part-year residency liabilities without necessarily becoming a permanent resident. My feeling (certainly not authoritative) would be their residency is the last established residency prior to becoming residence of another state. Confusing, but they start with IL, and if moored in OH long enough to meet OH residency on May 12, they are part-year residents of IL until May 12. If they are not moored in OH long enough to meet OH definitions, then move on to WI, and are there long enough to meet WI definitions on Jun 12, then they are IL PY residents until Jun 12th. If they are extremely mobile and never stay in any state long enough to be established as residents, then they are IL residents full-year. Most states are aggressive and skew their definitions to the maximum extent to assess revenue. However, I can't imagine any state being shrewd enough to capture these folks unless they register their boat or earn income in a given state. Registration requirements via days are most likely similar to residency requirements. Earning income is a dead giveaway, and if sufficiently large, will result in the taxpayer having to file a part-year or non-resident return. Associated with this question is a supreme court decision about taxing retirement income by a state when the source of the retirement is from another state. Can add complications to this situation.

To elaborate on my previous comment, if the the boat is Not registered in IL, that could present a difficult problem as residence in anotgher state will have to be established and ties to IL wil have to be severed. A PO Box in another state won't do it. If they are going to live on the boat, they would have to rent a slip at some marina and be able to show proof of rental and utility payments for the tax year. Vehicles, drivers' licenses, voting reg. should all be in the new state. There might be additional connections.

First, this is not my area of expertise, bur I do read a lot and it seems to me that this could be a fairly complex question. Find some detailed resources, which are available online, so you can pin down the key issues, then examine the facts & circumstances. Note: Selling your home, then buying a boat registered in a different state by itself does not change your principal residence.

In what state is the boat registered? If it is IL, that is your answer.