Now as I'm guessing most people here know, in an Alt History in which the American War of Independence fails this generally leads to a 'United North America' of the Canada's, and of the colonies south of that. This I can imagine is probably what would happen.
Though what happens next is ASB IMO. Generally what happens next is that the 'UNA' stays with Britain and in fact sometimes becomes 'Politically United' or something to that affect. To me this is ASB, all things considered I think that Britain wouldn't be able to keep hold of the North American colonies to a huge extent.
What I can imagine happening is, let's say after a failed AWI that a North American union of some sorts will come about and it is in fact given representation. This keeps the 'NAU' content but with a growing 'foreign' population as people immigrate to North America it begins to get slightly more distant from the motherland. I can imagine it would then slowly and peacefully break away from Britain.
If any organization such as a 'Commonwealth of Nations' is set up I can see the 'NAU' being a part of this, a major part in fact and keeping the Monarchy as a head of state (if in this TL there would still be a monarchy.)
What do you think? Am I right in thinking this?