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Stanton, Texas. Stanton is a city in and the county seat of Martin County, Texas, United States. The population was 2,492 at the 2010 census.
STANTON, TX. STANTON, TEXAS. Stanton, the county seat of Martin County, is on Interstate Highway 20 100 miles south of Lubbock in the southeastern part of the county. In 1881 the Texas and Pacific Railway built a two-story section house, a pump, and a water tank at a small settlement in Martin County then known as Grelton.