Diamond:
The Black Plague wipes 75% of Europe. In Scandinavia, northern Germany, and Ireland, European civilization survives, and those three regions eventually form Svearika, Germania, and Eriu. Islam spreads throughout southern, central, and eastern Europe; dead Al-Andalus is repopulated by settlers from the Maghrib and farther afield.
China discovers the Americas (The Sun Continents) by mistake in the mid-1600s AD and proceeds to make the Inca a vassal state. But plague ravages the New World, and China, thinking the land is cursed, mostly withdraws. In India, the progressive Mughal Empire and the southern Hindu Empire of Vijayanagara begin to industrialize and embark on their own age of exploration, colonizing vast tracts of southern Africa, Australia, and the South Pacific. Vijayanagaran sailors, blown off-course in 1760 or thereabouts, 're-discover' South America.
The western Muslims have not been idle either; Andalusian sailors discover and settle the islands of the Karib Sea in the 1740s; by 1850, the two Sun Continents of the New World are being steadily colonized by Indian and Muslim nations, and by a re-interested China. By this time the continents have come by their present-day names: *North America is known as Balad, loosely translated from Arabic as 'Wide Open Plain', while *South America is called Al-Ghala, or 'Land of Ghouls'.
Meanwhile, the natives of the Sun Continents have overcome the worst of their bouts with Old World sickness, and are rebuilding. Exploration and colonization is slower in this timeline, and many powerful and second-tier nations arise in the New World. The greatest of these are the Tawantinsuyu (the Inca), who, having been nearly destroyed by foreign plagues, develop into a near-fascist, xenophobic confederation, overthrowing their nobility; and the Houdenausee League, a democratic union of dozens of tribes and statelets from Vinland to the Misippah River.
The Chinese control most of western Balad, which is known as Fusang, as well as two colonies in far southern Balad, including Jinggu, whose mighty Great Canal allows transit between the Karib Sea and the Great Ocean.
In northern Al-Ghala, the land is a patchwork of Chinese- and Muslim-descended states. The culture here is unlike anything seen in OTL, as Chinese, Muslims, Tawantinsuyans, and dozens of other peoples interacted to form a society combining elements of each of their cultures. This was one of the heartlands of the Industrial Revolution (along with Egypt, the Ottoman Empire, and Vijayanagara), and its people have one of the highest standards of living on the planet.
In southern Al-Ghala, the Tawantinsuyu hold sway in the west, jealously guarding their mountain passes against the Qalabid Sultanate and the former Indian colonies in the southeast. In the far south, the Vijayanagara still hold the colony of Ghurala.
Back in Africa, Islam spread throughout most of the northern part of the continent. Here, the mighty Songhai and Egyptian Caliphates hold sway, while their smaller neighbors attempt to play the two giants against each other. To the south and east is an anomaly: the Kingdom of Ethiopia, the only majority-Christian nation outside of northern Europe. Eastern Africa is a patchwork of mixed Indian and Muslim states, while the Kongo Imperium, once an Andalusi vassal, controls the interior. The Imperium exists in a state of near-perpetual civil war, as dozens of contenders to the throne vie for control. At the southern tip of the continent lies Komalajamin, the jewel in the colonial crown of Vijayanagara.
They are united with Portugal. Aragon is independent, but is a minor power allied with the Triple Alliance.