What term is used to describe the american belief that the united states would come to control all or most of north america?
a. federalism
b. manifest destiny
c. unitarianism
d. continentalism

The term which best describes what you're talking about; the idea or beliefs of Americans that they will control all of North America eventually is the belief of Manifest Destiny - b. 

This belief was further increased when the American nation was expanding and increasing in size and prosperity over time. This also almost became true, but Canada as a nation was also developing a strong territorial claim.