We prove uniqueness of mild solutions in the class C([0,Tau); L(n/2 gamma-1)) 0<Tau <=infinity, for sub-critical quasi-geostrophic equations without assuming any smallness condition. As a consequence, any mild solution in C([0,infinity); L(2/2 gamma-1)) satisfies the regularity and decay properties given in the previous paper [4]. The proof is performed in the framework of Lorentz spaces.915762