Ultimately the 'New World' became new battleground for the Europeans powers struggling for land, gold and other resources. Initially, Spain was the dominant power in most of the New World. Portugal complains enough to get a Papal Bull giving them Brazil. In 1521 Hernando Cortez' ultimate defeat of Moctezuma II and the Aztecs was greatly aided with virulent diseases and Indian allies. Similarily invasion of the Inca and murder of their leader Atahualpa by Pizzaro in 1531 led to the pillaging of tremendous quantities of gold and silver for the Spanish treasury. England, France and other European powers covetted the wealth and developed various strategies, including piracy, to get the wealth of the 'New World'. Elizabeth I (ERI) was the most successful and launched England's naval might that eventually eclipsed Spain and France's power that led to the British Empire of Queen Victoria.
Spain sent secondary expeditions to find more gold in North America and the fabled Northwest Passage. Later, Spain will attempt to establish colonial footholds in the southern areas of North America, while England and France battled over the northern forests. Here is a summary of Spain's expansion into what is now the United States: