Ok, a map (loosely) inspired by one of the stories in the "Other Earths" (Jay Lake etc.) collection.
The UK held onto America, but the tail has come to wag the dog: the capital is now in North America. The monarchy was disposed with in the 1930s, but plenty of traces still remain: the old nobility lost little of their wealth in the political upheaval, the Prime Minister (more of a Presidential figure, power-wise, than OTL British Prime Ministers) when inaugurated is symbollically and briefly crowned with the crown of England and North America, and that bloody huge 1897 statue of the Queen Mother is still sitting in New York harbor.
The British monarchy hangs on in Australia, more populous (40 millions) and industrialized a country than OTL, but of late has become a quite cordial ally of the United Empire.
The Empire suffers from severe internal stress: the Scots are a bit of a pain, but far worse is middle America, where a theocratic rebellion from the late 90's on has only recently been brought to heel, and the horrific stress killed the previous president (who looked oddly like George Bush
) in late 2006. Even now, a huge patch of the country is still under martial law, and bombs still regularly go off across the country.
Not that the trouble was confined to the domestic situation. The Fascistic (and rather richer and more powerful than OTL) Chinese Empire took advantage of the situation to launch an invasion of the Formosan Republic and Japan (a less successful modernizer than in our world: currently about as rich per capita as Malaysia and with about 190 million inhabitants - some 10% fewer than before the invasion). Only thanks to Russian support (and, it must be admitted, Japanese intransigence) did China finally back down and accept a cease-fire.
Not that the US gets along well with Russia, either. Russia is a leftist dictatorship (although the syndicalist "union of workers cooperatives" is a more decentralized setup than our USSR - 100 little tyrants for every big one in our USSR, and a lot of behind-the-scenes dealmaking hidden by a united outwards front), and is always busy trying to undermine the position of the Empire in the middle east, where the biggest powers are leftist and pro-Russian. They also have an old grudge re eastern Siberia, which in a more successful "pro-white" intervention than OTL first became an Empire protectorate, and eventually a full part (it is currently English-Russian bilingual).
Syndicalist and theocratic unrest continue in Latin America and post-colonial Africa, although theocrats are a minor problem in mostly Catholic latin America outside of formerly British Guyana. A theocratic regime exists in East Africa, but it being an African country, most people don't take it any more seriously than they did Afghanistan OTL before 9/11. South Africa is Dutch-speaking, and after certain "resettlement programs", over 50% white, 'colored', and Asian. There is no Israel, but there was no holocaust in this world, and the Islamic world is not associated with fundamentalist violence in this world, although there have been rumblings in Africa and the Arabian peninsula. The Republic of North Arabia is the one big US ally in the middle eastern region, a right-wing arab nationalist state with atomic weapons, which contends for regional leadership with Iran and Egypt.
Other major US allies include Australia and the Union of the Southern Cross, a richer area than in OTL. India is generally friendly, but has internal problems of its own. Relations with the United States of Europe are often a bit prickly, cultural and political differences - as well as competition for market share - being constant irritants, as is the historical tendency of the Empire to act as if "The Wogs Begin at the Channel." They share a common interest in preventing the Russians from dominating the Middle East, but since bloodying the Syndicalist Union's nose in the Baltic War of '42-'44, they feel they can take care of themselves, and have gone a lot further than the US in moving towards atomic and other forms of alternate energy.
The United Empire was slow to give up slavery, including as it did large parts of the Caribbean as well as OTLs Confederate States, and full civil rights are as recent and the "boundaries" uncertain as they were OTL in the 1970s. They also have a "culture war" division rather worse than ours: besides a strong evangelical tradition with no-bones-about-it belief in creating a "Christian" nation, it also has a loudly athiestic, humanist, "new enlightenment" movement far more influential than Richard Dawkins and Co. OTL, which often descended into outright violence _before_ things went out of control in the late 90's. The new president is Hispanic, a "man of reason" to the rationalists, a devout Christian to the religious, and catholic (and therefore considered likely to maintain an appropriate distance between things that are Gods and those which are Ceasars). His challenges - to give American blacks more of a stake in the system, to reduce international tensions, and to heal the wounds of the recent conflict - are huge, but at least for now the violence of the last decade has alienated most Christian believers from the extremists.
One odd difference between this world and ours is the existence of a recent (last few centuries) genetic ailment known as "brain fever": those who have it tend to be extemely intelligent, as obsessively focused as the autistic or those with obsessive-compulsive disorders - and often dangerously sociopathic. Such people, since the mutation began to be identified as something different from demonic possession or general 'witchyness' in the 18th century, have been generally segregated from society, whether by being locked up, sterilized, killed...without too much protest from the mercy-minded, since they _have_ been responsible for some horrendous crimes. [1] There are rumors that many governments use them as a valuable intellectual resource, set loose on problems under carefully controlled conditions. Even the United Empire and the Europeans lock them up "for their own safety", although some success has been achieved in controlling their nastier personality quirks with medication.
Bruce
[1] People in this world would mistake "The Silence of the Lambs" for a documentary.