  We prove that faithful traces on separable and nuclear C*-algebras in the UCT
class are quasidiagonal. This has a number of consequences. Firstly, by results
of many hands, the classification of unital, separable, simple and nuclear
C*-algebras of finite nuclear dimension which satisfy the UCT is now complete.
Secondly, our result links the finite to the general version of the Toms-Winter
conjecture in the expected way and hence clarifies the relation between
decomposition rank and nuclear dimension. Finally, we confirm the Rosenberg
conjecture: discrete, amenable groups have quasidiagonal C*-algebras.
