Republic of Texas map

The Texas Congress set the borders in December 1836: the Sabine River on the east, the Red River on the north, and the Rio Grande from its mouth to its source, then due north to the 42nd parallel. That line swallowed the eastern half of present New Mexico (including Santa Fe and Albuquerque), a strip of Colorado, the Oklahoma panhandle, part of Kansas and a corner of Wyoming. Mexico never accepted any of it and still regarded Texas as a rebel province, with the Nueces River as the real southern limit.

In practice the Republic governed the settled east, between the Sabine and roughly the Colorado River, plus San Antonio. The 1841 Santa Fe Expedition, meant to assert the New Mexico claim, was captured by Mexican troops without a fight.

Settlement ran on the empresario system the Republic inherited from Mexico: a contractor took a block of land and undertook to put families on it. The Peters Colony, chartered in 1841, covered a wide block of north Texas along the Trinity, including the ground where Dallas and Fort Worth now stand. The Fisher–Miller grant, between the Llano and the Colorado, was taken up by a German emigration society whose settlers founded New Braunfels in 1845 and Fredericksburg in 1846, pushing the frontier into the Hill Country. Away from the grants nearly everyone lived in the timbered east and along the lower Brazos, Trinity and Colorado; the line of settlement ran roughly through Austin, and west of it the Comanche frontier held. The Republic never completed a census of its own — the first federal count, in 1850, found 212,592 people in Texas.

The Republic kept a small navy, based at Galveston, to hold the Mexican fleet off the coast and keep the sea lanes to New Orleans open; under Commodore Edwin Ward Moore the second fleet raided the Mexican coast and worked alongside rebels in Yucatán, and what survived passed to the U.S. Navy at annexation. Paying for the navy, the army and the frontier was the Republic's standing problem. It issued paper money that traded far below face value and borrowed against land it could not sell, and the debt outlived the country — which is what the payment below settled.

Annexation in 1845 carried the claims into the United States and triggered the Mexican–American War. The 1848 Treaty of Guadalupe Hidalgo fixed the Rio Grande as the international border, satisfying the southern claim. The northern arm was settled by the Compromise of 1850: Texas gave up everything north and west of its present boundary (about 67 million acres) in exchange for $10 million to pay the Republic's debt. That is why the Panhandle stops at 36°30′ and why the western border runs along the 103rd meridian instead of the Rio Grande.