Well, one of the reasons that the ARW happened was because the colonists weren't able to expand, so if they do ,it will be against Britain's will, which would probably lead to attempts for independence, which destroys the point of this thread a bit. Now, if the British won the war, I imagine the British will still prevent them from expanding and will let the territory go to the natives who fought on the British side and then they'll probably form their own state(s) that will be allies to the British. If I recall one of the reasons for why the Maori still have a not so terrible position in New Zealand is because the British really didn't want to support the colonists in fighting them, so they were forced to get along.
That's what's taught but in reality variances were already being granted with additional treaties, allowing the settlement of WV and Kentucky among others. Further adjustments would be made later if no ARW.
I agree with most of my colleagues. Basically OTL.