Aucencio, Name origin?
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I'd say Aucencio is most likely a variation of Ascensión.
Might be the original Latin form of the Spanish name?
It's likely a misspelling of Ausencio, male form of Ausencia, which means Absence. For a Spaniard, Ausencio and Aucencio are pronounced differently, but for Latin American Spanish speakers, c, z and s are both read alike so it's common to find American versions of Spanish given names and last names with the cs and zs jumbled up.