What agreement gave Spain most of North America and South America?

Answer 1

Treaty of Tordesillas. This treaty was signed by Spain and Portugal. It gave Spain the non-christian lands in North America and South America. But in exchange, Portugal received all of Spain's African territory. The only exception to this rule was that Portugal got modern-day Brazil. Every other country was mostly unaffected by the treaty. In 1493, after Columbus' voyage to the New World, Pope Alexander VI issued the decree "Inter caetera II" which divided the world from the North to the South Pole and granted Spain title to all lands to be discovered west of the line to assist in "the expansion of the Christian rule."

Answer 2

The "I kill anyone who rejects my authority" agreement. The Spanish weren't given the land: they took it.