Extremal richness of multiplier and corona algebras of simple C*-algebras with real rank zero

In this paper we investigate the extremal richness of the multiplier algebra M(A) and the corona algebra M(A)/A, for a simple C*-algebra A with real rank zero and stable rank one. We show that the space of extremal quasitraces and the scale of A contain enough information to determine whether M(A)IA is extremally rich. In detail, if the scale is finite, then M(A)IA is extremally rich. In important cases, and if the scale is not finite, extremal richness is characterized by a restrictive condition: the existence of only one infinite extremal quasitrace which is isolated in a convex sense.