  We show that, if A is a separable simple unital C*-algebra which absorbs the
Jiang-Su algebra Z tensorially and which has real rank zero and finite
decomposition rank, then A is tracially AF in the sense of Lin, without any
restriction on the tracial state space. As a consequence, the Elliott
conjecture is true for the class of C*-algebras as above which, additionally,
satisfy the Universal Coefficients Theorem. In particular, such algebras are
completely determined by their ordered K-theory. They are approximately
homogeneous of topological dimension less than or equal to 3, approximately
subhomogeneous of topological dimension at most 2 and their decomposition rank
also is no greater than 2.
