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We prove that both stated skein algebras and their reduced versions at oddroots of unity are almost-Azumaya and compute the rank of a reduced statedskein algebra over its center, extending a theorem of Frohman,Kania-Bartoszynska and L\^e to the case of open punctured surfaces. We deducethat generic irreducible representations of the reduced stated skein algebrasare of quantum Teichm\"uller type and, conversely, that generic quantumTeichm\"uller type representations are irreducible.

Unicity for representations of reduced stated skein algebras