  Suppose B is an ultraproduct of finite dimensional C^\ast-algebras. We
consider mapping and injectability properties for separable C^\ast-algebras
into B. In the case of approximately finite C^\ast-algebras, we obtain a
classification of these mappings up to inner conjugacy. Using a Theorem of
Voiculescu, we show that for nuclear C^\ast-algebras injectability into an
ultraproduct of finite dimensional C^\ast-algebras is equivalent to
quasidiagonality.
