Let's start in the United States.
In OTL, immediately before and after the War of 1812, the American Colonization Society organized the settlement of Africans in British Sierra Leone. Let's assume they decide early on to continue this, allowing more money to go to actual emigration as opposed to land ownership.
In 1820 a slave rebellion in Virginia results in mass anti-black legislation throughout the United States. In the North, it kicks off the laws that will evolve into the OTL Jim Crow system. In the South, laws mandate the expulsion of free blacks from the states. This happened in 1831 in OTL, but 11 years earlier, the memory of hostile ships sailing just off the coast is still fresh. Both sets of laws are more thoroughly enforced.
Hundreds and then thousands of blacks begin to travel across the Atlantic to Freetown. The cities position on a peninsula gives it a marginally better disease environment, so a greater proportion of these people survive and acclimate to their new home.
The year 1820 is also significant in that it marks the assassination of Muhammad Ali in Egypt. With his efforts to create a dynasty (and a de facto independent state for it) still in their infancy, Egypt stumbles through a succession of unrelated rulers for the next half-decade. Eventually a governor decides to keep his place by being more than a de jure vassal, and invites the Ottomans back in.
Fast-forward through a vaguely familiar course of history and you have, in 1880, a world we can somewhat understand: The United States includes the better than half of old Mexico and has weathered a six-year civil war in the mid/late '60s. A Suez Canal - owned by France and Britain cuts the Ottoman Empire into two parts. Germany and Italy exist, Belgium doesn't. The latter have interests in bits of Namibia and Somalia, respectively. France is in Algeria. Portugal's colonies are still where they've always been. The Boer States dislike the British, who are in the Cape and Natal.
Quite a bit is less recognizable: The Ottomans rule deep into the Sudan and Chad; they retain Tunis and a Balkan Peninsula that is developing a strong Muslim majority as Christians emigrate and Muslims come in from the rest of the empire (this is a conservative assumptions that they do little better than OTL). France has only been in Algeria for 10 years, not 50. Around the world Malaria is much less lethal. A proto-state is forming in OTL Sierra Leone and Liberia, and has good relations with some neighboring groups. The Boers are actively inviting in non-English whites, and granting them full rights. Italy includes Trieste and a smidgen of Tyrol.
As in OTL, the Scramble is driven by Germany's effort to "catch up," and a sense by the other powers that once it's started they must get "their share." When Portugal goes bankrupt in 1891, it's colonies are divided between Britain, France, and Germany. Of note is Angola, which goes to Germany. In exchange for the better portion, Germany makes concessions: Southwest Africa south of Walvis Bay is added to British South Africa. France is acknowledged to have full right and privilege to the entire Congo Basin. The Ottomans could potentially grab a lot, but luck out at having nothing actually taken from them. The best they manage is British acknowledgement of their nominal overlordship over Sokoto - the northern 2/3 of Nigeria.
Beginning in the 1910s, Ottoman rule in distant parts of Africa and Arabia has become more formal. In the process they've found themselves compromising on the level of autonomy of their far-distant new provinces. Simultaneously, growing local democracy and literacy has increasingly made the empire's core aware of it's diminishing seniority. The result is a long series of efforts to achieve local autonomy. Over the course of the next thirty years the Empire, long-since a constitutional monarchy, transforms itself. By the end of the Great War it is a tight economic union with reliable structure for operating mutual defense, railroad-building, mail services, and the like. But otherwise, though, it is a fairly autonomous confederation.
Off in the distance, the Zanzibar Dominions follow, with aching slowness, the Ottoman model.
A decade and a half later the Federation of South Africa forms peacefully, consisting of a lower house with members elected from white-ruled states and an upper with more of the same, plus two representatives from each black state. Over the next 20 years it spreads from central Namibia northeast to Zambia and Mozambique.
In 1930, the Great War breaks out. Italy, Germany, and Austria-Hungary face Russia, France, and Britain. The Ottomans remain carefully neutral, once they've squeezed enough promises out of Britain and France. Initially the war goes even worse for the Entente. A series of naval victories in the Mediterranean, raids on the Tuscan coast, and the eventual invasion of Sicily fail to counter the back-and-forth assaults gradually expanding further onto French and Russian soil. In the midst of the chaos, the Ethiopian descent on Italian Northwest Somalia is little-noted. Finally American entry on the side of the Entente settles the matter.
The war's end sees German colonies divided. Most of Angola goes to the French-run Congo, with the extreme south and northern Namibia turned over to South Africa. In West Africa the conquest of intervening German colonies starts the first serious talk of federation. The Ottomans had their neutrality paid for in part with African promises, and win big. They expand into parts of the French Sahel/Sudan/Whatchamacallit and formalize their. Ethiopia's new coastline is confirmed.
Decolonization comes slowly, completing in the late 1970s. By then the Ottomans and French have nearly come to blows twice over Islamic Africa's preference in distant ruler. Africa has tremendous problems, most notably the huge and ungainly states comprising it. The new Republique du Congo, Federation of South Africa, and United Kingdoms of West Africa are all tremendously conflicted states. Not a one can easily administer all of its areas, and even the nominally unitary Congo ends up with a slew of autonomous departments in central Africa and old Angola.
Still, the problems for the smaller states - those we'd recognize from OTL - are still greater. States with a single central city are more vulnerable to coups. States with only two ethnic or religious groups find politics polarized along those lines. Small states also tend to develop more limited infrastructure.
The result is a slow trend between 1980 and 2010 that sees the small states of West and Central Africa instigating bidding wars between the three great post-colonial states. In early 2010 a formal referendum in Benin sees it joining the UKWA. It is the last small, or indeed medium state in Africa. Even the smaller remaining states - Cameroon, Ethiopia, Zanzibar - are each larger in land area than Spain.
Fin.