Wikipedia
Astete is a Spanish surname, from an ancient Basque - Castilian lineage. The etymology of "Astete" comes from the Basque language: "Aste" possibly a variation of "Arte" means oak, and "ete" is a suffix to nearby location. The most probable original locations, prior to the 16th century, are the regions of ancient Basque influence of the medieval Castile (such as La Bureba and the mountains of Burgos) and modern La Rioja. The earliest official records of Astetes occur in La Rioja, in Santo Domingo de la Calzada, in the province of Valladolid and Quintanaélez in the province of Burgos. They were hidalgos and had casas solariegas (ancient family seat) in Quintanaélez (Burgos), Valladolid and Salamanca.
The first immigrants to the Americas traveled there with expeditions in the 16th century. Today people of these surnames live mainly in Peru (the oldest branch), Chile, Bolivia, Argentina, Brazil, Mexico and United States. In Spain the surname is very rare today. Most Spanish Astete are descended from the branch that settled in Seville, Zahara de la Sierra and Grazalema (between the 17th and 18th centuries), and live in the province of Cádiz in Andalusia. The variant "Estete" is possibly from La Rioja, but occurred sporadically or as a result of spelling mistakes in other Spanish provinces.