Question: What was the capital of the union of provinces in the Río de la Plata comprised by most of the former dependencies from the last to be organized and also the shortest-lived of the Viceroyalties of the Spanish Empire in the Americas?

Documents:
source: Viceroyalty of the Río de la Plata
text: Viceroyalty of the Río de la Plata The Viceroyalty of the Río de la Plata (Spanish: "Virreinato del Río de la Plata" ) was the last to be organized and also the shortest-lived of the Viceroyalties of the Spanish Empire in the Americas.

source: United Provinces of the Rio de la Plata
text: United Provinces of the Rio de la Plata The United Provinces of the Río de la Plata (Spanish: "Provincias Unidas del Río de la Plata" ), earlier known as the United Provinces of South America (Spanish: "Provincias Unidas de Sudamérica" ), a union of provinces in the Río de la Plata region of South America, emerged from the May Revolution in 1810 and the Argentine War of Independence of 1810–1818. It comprised most of the former Viceroyalty of the Río de la Plata dependencies and had Buenos Aires as its capital.

source: Santiago de Liniers, 1st Count of Buenos Aires
text: Santiago de Liniers, 1st Count of Buenos Aires Jacques de Liniers (July 25, 1753 – August 26, 1810) was a French officer in the Spanish military service, and a viceroy of the Spanish colonies of the Viceroyalty of the Río de la Plata. He is more widely known by the Spanish form of his name, Santiago de Liniers. He was popularly regarded as the hero of the reconquest of Buenos Aires after the first British invasion of the Río de la Plata, which led to his designation as viceroy, replacing Rafael de Sobremonte. Such a thing, the replacement of a viceroy without the King's direct intervention, was completely unprecedented. He was confirmed in office by Charles IV of Spain, and endured a second ill-fated British Invasion attempt and a mutiny that sought to replace him. He was replaced in 1809 by Baltasar Hidalgo de Cisneros, appointed as viceroy by the Junta of Seville, and retired from public activity. However, when the May Revolution took place, Liniers decided to come out of his retirement and organized a monarchist uprising in Córdoba. However, Liniers was defeated, captured, and executed without trial.

source: Governorate of the Río de la Plata
text: Governorate of the Río de la Plata The Governorate of the Río de la Plata (1549−1776) (Spanish: "Gobernación del Río de la Plata" ) was one of the governorates of the Spanish Empire. It was created in 1549 by Spain in the area around the Río de la Plata.

source: Battle of Sipe-Sipe
text: Battle of Sipe-Sipe The Battle of Sipe-Sipe (also known as Battle of Viluma among Spanish historians) was a major battle in the South American wars of independence in which the United Provinces of Río de la Plata (formerly the Spanish Viceroyalty of the Río de la Plata) were decisively defeated by Spanish royalist forces in Upper Peru (now Bolivia). The battle took place on November 29, 1815, and resulted in the loss of Upper Peru for Buenos Aires. The area was reannexed by the Spanish Viceroyalty of Peru.

source: Río de la Plata
text: Río de la Plata The Río de la Plata (] , "River of Silver") — rendered River Plate in British English and the Commonwealth and La Plata River (occasionally Plata River) in other English-speaking countries — is the river and estuary formed by the confluence of the Uruguay and the Paraná rivers. It empties into the Atlantic Ocean, forming a funnel-shaped indentation on the southeastern coastline of South America. Depending on the geographer, the "Río de la Plata" may be considered a river, an estuary, a gulf or a marginal sea. For those who consider it a river—as is the case in most of Argentina and Uruguay—it is the widest river in the world, with a maximum width of about 220 km .

source: Governorate of Paraguay
text: Governorate of Paraguay The Governorate of Paraguay (Spanish: "Gobernación del Paraguay" ), originally called the Governorate of Guayrá, was a governorate of the Spanish Empire and part of the Viceroyalty of Peru. Its seat was the city of Asunción; its territory roughly encompassed the modern day country of Paraguay. The Governorate was created in December 16, 1617 by the royal decree of King Philip III as a split of the Governorate of the Río de la Plata and of Paraguay into its respective halves. The Governorate lasted until 1782, after which the massive Viceroyalty of Peru was split, and Paraguay became an intendency ("intendencia") of the new Viceroyalty of the Río de la Plata.

source: List of heads of state of Argentina
text: List of heads of state of Argentina Argentina has had many different types of heads of state, as well as many different types of government. During Pre-Columbian times the territories that today form Argentina were inhabited by nomadic tribes, without any defined government. During the Spanish colonization of the Americas, the King of Spain retained the ultimate authority over the territories conquered in the New World, appointing viceroys for local government. The territories that would later become Argentina were first part of the Viceroyalty of Peru, and then the Viceroyalty of the Río de la Plata. The May Revolution started the Argentine War of Independence by replacing the viceroy Baltasar Hidalgo de Cisneros with the first national government. It was the Primera Junta, a junta of several members, which would grow into the Junta Grande with the incorporation of provincial deputies. The size of the Juntas gave room to internal political disputes among their members, so they were replaced by the First and Second Triumvirate, of three members. The Assembly of the Year XIII created a new executive authority, with attributions similar to that of a head of state, called the Supreme Director of the United Provinces of the Río de la Plata. A second Assembly, the Congress of Tucumán, declared independence in 1816 and promulgated the Argentine Constitution of 1819. However, this constitution was repealed during armed conflicts between the central government and the "Federal League" Provinces. This started a period known as the "Anarchy of the Year XX", when Argentina lacked any type of head of state.

source: Matanza River
text: Matanza River The Matanza River is known by several names, including, in Spanish, Río de la Matanza ("the slaughter river" in English), Río Matanza ("slaughter river"), Río Mataderos ("slaughterhouses river"), Río de la Manzana ("the apple river") or simply Riachuelo ("little river" or "brook"). It is a 64 km stream in Argentina that originates in the Buenos Aires Province and defines the southern boundary of the Buenos Aires federal district. It empties into the Río de la Plata between Tandanor and Dock Sud. The La Boca neighbourhood and the Boca Juniors football club are located near the Riachuelo's mouth. The Spanish word "boca" means "mouth".

source: Real Audiencia of Charcas
text: Real Audiencia of Charcas The Real Audiencia of Charcas (Spanish: "Audiencia y Cancillería Real de La Plata de los Charcas" ) was a Spanish "audiencia" with its seat in what is today Bolivia. It was established in 1559 in Ciudad de la Plata de Nuevo Toledo (later Charcas, today Sucre) and had jurisdiction over Charcas, Paraguay and the Governorate of the Río de la Plata, today Uruguay and northern Argentina. This court oversaw the incredible silver output of the mines at Potosí. It was part of the Viceroyalty of Peru until 1776, when it was transferred to the newly created Viceroyalty of the Río de la Plata and began to be referred to as Upper Peru.

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Answer: Buenos Aires