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I am currently visiting the USA from the UK (I am a UK citizen) and am intending on staying here for the full 90 days under the Visa Waiver Program.

How long would I have to stay out of the US at the end of this period before returning again?

Would I have to return to the UK, or could I stay with friends in another country (such as Canada) for a while?

It all comes down to a 'reasonable length of time' between stays.

Now that's about as ambiguous as they come - what's reasonable? It's like this on purpose - it's up to the official at the border, as the purpose of this is to try and work out if you're trying to live in the states and just border hopping every 90 days, instead of visiting.

From the CBP website:

When traveling to the U.S. with the approved ESTA, you may only stay
for up to 90 days at a time - and there should be a reasonable amount
of time between visits so that the CBP Officer does not think you are
trying to live here. There is no set requirement for how long you must
wait between visits.

If you're worried they may think you're trying to live there, then you could bring extra documents as evidence - eg, your flight out of America back to the UK, or proof of your current employment and residence in the UK. Basically anything to convince them that you're not actually surreptitiously residing in the US :)

Note that going to islands or Canada doesn't reset it, as found on most US embassy websites:

"The Visa Waiver Program (VWP) enables nationals of certain countries, including Australia, New Zealand, and the U.K., to travel to the United States for tourism or business for stays of 90 days or less without obtaining a visa, if certain requirements are met. Under the VWP, time spent in Canada, Mexico, and adjacent islands counts towards the maximum of 90 days stay allowed under the program."

Short version - it doesn't matter, what matters is convincing the border officer that you're visiting, not living in the US.

If you go to Canada and Mexico or the Caribbean, and while you are there, your initial 90-day period of entry expires, but you need to come back in to the U.S. to fly home, you may encounter a problem. The terms of the VWP are very clear - it is only to be used for occasional, short visits to the U.S. If the CBP Officer thinks you are trying to "reset" the clock by making a short trip out of the U.S. and re-entering for another 90-day period, you can be denied entry. (If that happens, you will have to obtain a visa for any future travel to the U.S.) In order to be re-admitted to the U.S. shortly after a previous admission expired, you will have to convince a CBP Officer that you are not trying to "game" the system.

https://help.cbp.gov/app/answers/detail/a_id/194/kw/90%20days

(as of 25 Mar 2015)

https://travel.stackexchange.com/a/61835/4188 has the answer.

the important paragraph reads:

The Visa Waiver Program doesn't work that way. If he decides to use the Visa Waiver Program (ESTA); maximum stay is 90 days and he needs to allow adequate time between visits. The rule of thumb is if he is in the US for 90 days; should be out of the U.S. for 91 days before returning.

It's not an official regulation but a "rule of thumb".

There is no official rule on this. It is up to the discretion of the customs office dealing with you at the border to decide if you can or can't enter. This applies whether you have a visa or wish to use the Visa Waiver Program (VWP).

The prime directive of the officer is to assume you wish to permanently live in the USA (i.e. immigrate there). It is up to you to prove otherwise. The amount of "proof" required may be as simple as your verbal statement that you intend to do XYZ whilst there, and intend to leave on XYZ date. Yet there are scenarios that tend to trigger suspicion at boarder control. For example, if the records show you have been spending more time in the USA than you have outside the USA, the officer may decide you are misusing the VWP system to "live" in the USA. Another example, if you have previously stayed in the US for a maximum 90 days on the VWP, and then you return, let's say, within 12 months of your previous entry (although, it's totally at the discretion of the officer you deal with) this can alert them to questioning you more throughly. I know of numerous first-hand cases when that second scenario has played out. One was a friend from Sweden who stayed 89 days on the VWP. She returned 11 months later, to visit for another 80 to 90 days (which she told the officer), and she was taken aside for 3.5 hours of searching and questioning. She missed her connecting flight, and had to go to great lengths to convince them she had zero intention or desire to immigrate there.

My personal experience is that some ports of entry have officers with significantly stricter attitudes. Others are more relaxed. For instance, in my experience, the difference between entering the USA via Florida and New York is like night and day. I've entered through both on many occasions. I've also noticed a significant difference between LAX and SFO when entering on the West coast. Although, I will say recent (2015 to 2017) experience at LAX has been more relaxed. I always come and go through SFO if possible. It's not as much of a difference as MIA and FLL (both in Florida), but enough to warrant avoiding LAX and NYC if possible. Also the airport is less busy in SFO so that's a plus.

It is my understanding that if you are denied entry you will require a visa to return to the USA (and this will hold true for a period of 10 years). Receiving a visa may also be more difficult if you were refused entry at the border. You will likely have to go to much greater lengths (if even possible) to prove the validity of your reasons for visiting the USA, and applying for a visa. Caution is advised.