by @Chris
In 1808 South America belonged to two crowns: Spain's viceroyalties and Portugal's Brazil. Napoleon's invasion of Iberia broke both. This map follows what came next, year by year through the wars of independence (the juntas of 1810, the royalist reconquest, San Martín over the Andes, Bolívar from the Orinoco to Potosí, Ayacucho) and then through two centuries of republics: Gran Colombia and the Peru–Bolivian Confederation breaking up, Uruguay born as a buffer state, Paraguay cut down in 1870, Bolivia losing its coast and Peru its nitrate south to Chile, the conquest of Patagonia, Araucanía and the Chaco, Acre, Panama, the Chaco War, the Rio Protocol and the Falklands. Simplifications: territories follow modern provincial borders with hand-drawn cuts where the old line ran elsewhere. Colours show who actually held the land where that is known (royalist or patriot armies, occupations); in the empty Amazon they follow the generally mapped claims, and the indigenous south is shown as free until the state conquered it. Small disputes (Amapá, Pirara, Palmas, the Beagle islands, Essequibo) appear as markers only. Frontier lines in the pampas and the pre-war lines in the Chaco and the upper Amazon are approximate. Sources: Wikipedia articles on the Spanish American wars of independence and on each war, treaty and arbitration named in the markers; Natural Earth borders.
Spanish Empire (royalist-held) · Portuguese Brazil · Empire of Brazil → Brazil (republic 1889) · United Provinces of the Río de la Plata → Argentina · State of Buenos Aires (1852–61) · Federal League of Artigas (1814–20) · Uruguay · Paraguay · Chile · Peru · Bolivia · Peru–Bolivian Confederation (1836–39) · Gran Colombia (1819–30) → New Granada → Colombia · Venezuela · Quito and Guayaquil juntas → Ecuador · Panama · Riograndense Republic (1836–45) · British Guiana and the Falkland Islands · Guyana · Dutch Guiana · Suriname · French Guiana · Indigenous land beyond state control