Just a try...
-15th century
Holy Roman Empire (or Prussia, or Germany, or whatever) united/centralized much earlier, Iberian Union succeed, and Ottoman Empire industrialized/westernized. Together with Britain and France, those three empires engaged in colonial race during Discovery Age.
-16th century
France conquered the Aztecs, Holy Roman Empire conquered the Incas, Iberia colonized Brazil, Britain colonized North America, while Ottoman East India Company dominated the East Indies (Sweden became minor colonial power by colonized Greenland and Iceland).
-18th century
In an ATL analogue of Seven Years War, Britain-Russia-Ottoman Empire alliance defeated France-Iberia-Holy Roman Empire alliance. Britain get Argentina (as well as domination over China), Russia get Japan, and Ottoman Empire get Italy. However, Iberia and France retained its domination over Persian Gulf and India respectively, while Holy Roman Empire shifted its attention to Indochina. ATL analogue of American Revolutionary War was crushed.
-19th century
Scramble of Africa (and Asia) began.
-20th century
All global empires gradually evolved into federal unions or commonwealths (instead of decolonization).
Cool enough for a TL, huh?
