Okay so this next map to go with my wee series took me a little while. I haven't conveyed as much information as I would have liked, but if I had it would be too big or too cluttered.
--
The United Kingdom of Great Britain, Ireland and the Faroes (tagged to the end after annexation following the German annexation of Denmark).
UK history didn't diverge that much from OTL. Aside from meddling a little bit more in the Americas (a bigger Guyana, annexing all of the Lesser Antilles, allying itself with California) Britain has pretty much followed the same route as OTL - get bigger, and bigger! AND BIGGER!
This British Empire is actually smaller than OTL's, in saying it got bigger, as it lucked out a lot when it came to certain areas. After the 1860s Britain took a little while to recover from its economic crisis, shrugging off a few colonies in the process, but they still managed to make some substantial gains in Africa. The Suez Canal is undoubtedly the most important, and East Africa is looking to be the next South Africa as far as white settlement is going.
India is a little different ITTL as well. The British did better in the west, but Siam, stronger and more capable at playing Britain and Germany off than it was between France and Britain OTL, stifled a lot of expansion in the east. Britain was, however, able to absorb Tibet into the Raj's fold, giving China a headache big enough to cause near civil war.
Britain also beat the Netherlands to Borneo, and pretty much forced the Dutch out of whatever scraps they had left. It worked out well for the British, who now have two valuable colonies in the Far East.
Western Australia, unlike the east, opted out of dominionship; they are not populous, the mines aren't as valuable as they once were, and the two sides are growing more culturally different every year.
On the bright side, Australia is a lot more conservationally-minded ITTL, and the dwindling numbers of nail-tail wallabies and thylacines are steadily on the rise. Similarly, the emu was reintroduced to Tasmania after being virtually wiped out in the 1880s.