First,
Kaiphranos:
South America, 1825
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In this world, the Bourbon Reforms of the 18th century turned out slightly differently--most notably, the borders between the Viceroyalty of Peru and the new Viceroyalty of the Río de la Plata were drawn somewhat differently, with most of Upper Peru remaining with the former. The French Revolution and the Napoleonic Wars occur much as they did in our world, but the Latin American wars of independence proceeded differently, as the differences in the Bourbon reforms resulted in some different dynamics within the three Viceroyalties of New Granada, Peru, and the Río de la Plata. Paraguay does not secede from La Plata, and the Royalist position in Peru is stronger.
In fact, Spain never quite loses control of the Viceroyalty of Peru, although the end of the wars in 1825 sees new independent republics in Chile, New Granada (renamed Gran Colombia) and the new United Provinces of the Río de la Plata.
Two of these three were fated not to last. As in our world, Venezuelans grew dissatisfied with their position within Gran Colombia, but in this world their grievances were left to simmer longer, and rather than peacefully dissolving into its constituent pieces, the Gran Colombian government fought a bloody and unsuccessful war to prevent Venezuela from leaving.
The United Provinces fared somewhat better for a time. Larger and stronger than the Argentine Confederation of our world, it fared better in a war against Brazil, recovering the lost Banda Oriental as well as a chunk of Mato Grosso province. But as in our world, there was tension between Federalist and Unitarian factions regarding the influence of Buenos Aires and the revenues it generated. The Federalists, strongest in the richer southern provinces, wanted to retain these revenues, while the northern provinces wanted a unitary government that would distribute them more evenly.
An rather odd war followed, in which the south basically fought to expel the northern provinces. These formed the Confederation of Tucumán, Paraná, and Paraguay, more commonly known as the Paranian Confederation. Ironically, without the prize of Buenos Aires, the former Unitarians found that a federal model better suited their new nation, while the United Provinces have become increasingly centralized.
Chile, alone of the new republics, managed to avoid any wars, but its leaders were less foresightful than our world, and Chile failed to establish claims to the area around the Straits of Magellan. Instead, these and much of uninhabited Patagonia fell to the French government, who established a number of settlements in the area, following the recommendations of the French explorer Jules d'Urville. Britain, which had also expressed interest in the region, had to satisfy itself with the Falkland Islands, re-establishing its earlier claim while the United Provinces were otherwise occupied.
Now, 50 years after the end of the wars of independence, the course of South American history has diverged significantly from our world... and will diverge further in just a few years with the untimely death of Dom Pedro II of Brazil...
First map: