How did the Spanish claim almost all of South America, Large Parts of the Caribbean, Central America, and Mexico so quickly I know that they conquered the Incans and the Aztecs which controlled large parts of the New World but still when i hear about it it is like conquest boom Most of the new world while the anglo-french are taking centuries just to get the St.lawernece and eastern seaboard. but the french even contridicted themselves by taking forever to get Canada set up and then boom all of Louisiana. Because surely the Spanish didn't have enough migrants to the new world to populate the colonies that they controlled and because france and england didn't recognize the popes law to give everything 100 leagues west from the azores to Portugal and everything else to spain would english and spanish look very different as they disputed the land in the new world
I'd like to direct you to this AMA and some other posts by myself and /u/400-rabbits to challenge the notion of a quick colonial expansion. It took hundreds of years for most of Latin America to come under Spanish control, rather than just Spanish "claim." The last Maya city lost independence 200 years after contact; the last holdouts in southern South America, which even the Inca couldn't conquer, effectively outlasted the entire Spanish colonial period.
The post from Mr. Rabbits is particularly useful from a comparative standpoint. In areas where there was already a subjugated populace, like central Mexico, the Spanish were able to slip into the role of the previous leaders. The locals were already paying tribute to the Aztecs, so the transition of power wasn't as dramatic as it would seem.