The mods may want to put this in P&E and I would not mind, but assuming there is a factual answer I prefer to start here.
And the title states it already: even if “Canada” or “the Canadians” or the Canadian Paliament or the Prime Minister or the King of England wanted to, there is no way Canada can adhere as a state to the United States South of them, is there?
So even if Trump strong-armed the country with tariffs and economic hardship up to the point where “they” had no other option but to beg for being colonized, or absorbed, or assimilated, or whatever you whish to call the result, they could not do it! It would be illegal and therefore have no validity.
Is the way I interpret this correct?
Wikipedia has a page on how a region can be admitted as a state.
Admission to the Union is provided by the Admissions Clause of the United States Constitution in Article IV, Section 3, Clause 1, which authorizes the United States Congress to admit new states into the Union beyond the thirteen states that already existed when the Constitution came into effect. The Constitution went into effect on June 21, 1788, in the nine states that had ratified it, and the U.S. federal government began operations under it on March 4, 1789, when it was in effect in 11 out of the 13 states.[1] Since then, 37 states have been admitted into the Union. Each new state has been admitted on an equal footing with those already in existence.
Is the OP asking how it would handled legally on the US end, or the Canadian / Commonwealth / UK end?
In general for any two entities, once there’s a mutual will to merge, any legal obstacles on either side will be legislated around.
There’s precedent. Four of the present United States (Vermont, Texas, California, Hawaii) were independent countries before they joined the union as states. So procedures certainly exist.
A cursory Internet search suggests that it would take a unanimous vote of the Canadian Parliament. While technically possible, it sounds like it might be pretty tough to actually accomplish.
Becoming a state is actually pretty easy. All it requires is Congress enacts a law. (Which, for those who didn’t watch Schoolhouse Rock, means a majority of the members of the House and the Senate vote in favor of it and then the President signs it.)
Historically, Congress has only made a region into a state when there has been an indication that the people in that region want to be a state. But there is no legal barrier to Congress imposing statehood even on a region that doesn’t want it.
For the umpteenth time in these threads, there is no Commonwealth or UK side. The Commonwealth is a club of countries with a common history. King Charles is the King of Canada independently of the King of Great Britain. Since we repatriated the Constitution in 1982, there are no legal ties to the UK.
If Canada voted to join the US, he would have no say in the matter. If the Governor General refused to sign any required legislation, we would have a constitutional crisis and join the US anyway. Not that it will ever happen.
Like, or un-like DC
Even if Canada did have legal ties to the UK, it wouldn’t make a difference.
Let’s say Wales decided to become a state of the United States. Once the United States enacted a law making Wales part of the United States, that act severs all existing legal ties with the United Kingdom. The fact that Wales becoming a state is illegal under British law is irrelevant because Wales is no longer subject to British law.
Obviously the United Kingdom might not see things the same way. But that would be an issue to be resolved by a war not by a legal dispute. The parallel here would be the situation in 1861 when eleven American states decided they were no longer part of the United States. The United States disagreed and said those states were still part of the United States. The dispute was resolved by a war, which ended up affirming the United States’ opinion on the subject.
My point is people keep bringing up this red herring with Canada/UK/Commonwealth. It’s nonsense. Canada has nothing legally binding us to the UK other than history and a monarchy in common.
I’m againt it happening. But if it were to happen, wouldn’t it make more sense to make each province a state? Because if Canada were one state, it would be a, um… big state.
The Canadian end. @Ynnad claims that it requires a unanimous vote of the Canadian Parliament. I wonder: who would bring the vote in, who would ratify/certify the vote, how would Canada procedually dissolve, how would it be integrated into the USA (and as how many states, and who decides about that, and with what weight in the Electoral College and in Congress), what would happen to Quebec’s linguistical status, particularly now that some guy wants to make English the official language of the USA… things like these. I have the feeling it is not possible and state so in my OP, but I may be wrong.
That’s the position under US law. You’ve also mentioned the position under UK law. And lastly, there’s the position under international law, which also has a thing or two to say about this: Countries cannot just unilaterally annex other countries or parts of other countries against their will. There’s a law being fought in Ukraine right now over exactly this issue.
Prince Edward Island has only 180,000 people, which would make it dramatically smaller than even the least populated state, and makes it dramatically smaller than any other province.
If this is a shotgun marriage, then good bet the goal of the Americans & their government is for former Canada to have the least political power possible. Making it a single state minimizes the number for US senators they get.
Meanwhile, it would probably be the goal of the Canadians to have as much political power as possible, whether they were forced into the USA at shotgun-point or came in happily and willingly and eagerly. In another thread I joked about chopping old Canada up into new US states each the size of Rhode Island so they’d be the vast majority of the newly combined senators and representatives. 
The U.S. Constitution guarantees each state shall have a republican form of government. So if Canada became a state it could not have a king (or a queen). The Canadian Constitution Act of 1982 prohibits any change in the position of the monarch in the Canadian government without the unanimous consent of the Parliament.
Big geographically obviously. But the state of Canada would still be second in population to California.
Canada has more people than California.
California’s population is 39,431,263. Canada’s population is 41,465,298.
I think it’s more accurate to say a country unilaterally annexing another country is frowned upon.
Yes, other non-involved countries might object and cite international law. But that doesn’t mean the annexation wouldn’t occur. History has shown otherwise on countless occasions.