What was the outcome of Texas breaking away from Mexico?

When Texas declared its independence from Mexico in 1836, it effectively became an independent nation known as the Republic of Texas. This outcome was significant as it marked a decisive shift in Texas' political status, separating it from Mexican governance. Following its independence, Texas operated as a sovereign nation until it was later annexed by the United States in 1845. This period of independence solidified Texas's identity and created a foundation for its future relationship with both Mexico and the United States.

The other options represent scenarios that did not occur—Texas did not become a province of the United States immediately after it broke away from Mexico, nor did it join the European Union, which did not exist at that time. Additionally, Texas's independence meant it was no longer under Mexican control. Therefore, the acknowledgment of Texas as an independent nation is the correct and historically accurate outcome.