  The Jiang--Su algebra Z has come to prominence in the classification program
for nuclear C*-algebras of late, due primarily to the fact that Elliott's
classification conjecture predicts that all simple, separable, and nuclear
C*-algebras with unperforated K-theory will absorb Z tensorially (i.e., will be
Z-stable). There exist counterexamples which suggest that the conjecture will
only hold for simple, nuclear, separable and Z-stable C*-algebras. We prove
that virtually all classes of nuclear C*-algebras for which the Elliott
conjecture has been confirmed so far, consist of Z-stable C*-algebras. This
result follows in large part from the following theorem, also proved herein:
separable and approximately divisible C*-algebras are Z-stable.
