After the U.S. army occupied Mexico City, the Treaty of Guadalupe Hidalgo was negotiated and brought the war to an end. The treaty gave the United States control of Texas, established the border at the Rio Grande, and ceded other Mexican lands to the United States in the southwest.
"We didn't cross the border; the border crossed us." (APEX)
the exclusive possession or control of the supply or trade in a commodity or service.