  We present a systematic discussion of supersymmetric solutions of 2D dilaton
supergravity. In particular those solutions which retain at least half of the
supersymmetries are ground states with respect to the bosonic Casimir function
(essentially the ADM mass). Nevertheless, by tuning the prepotential
appropriately, black hole solutions may emerge with an arbitrary number of
Killing horizons. The absence of dilatino and gravitino hair is proven.
Moreover, the impossibility of supersymmetric dS ground states and of
nonextremal black holes is confirmed, even in the presence of a dilaton. In
these derivations the knowledge of the general analytic solution of 2D dilaton
supergravity plays an important role. The latter result is addressed in the
more general context of gPSMs which have no supergravity interpretation.
  Finally it is demonstrated that the inclusion of non-minimally coupled
matter, a step which is already nontrivial by itself, does not change these
features in an essential way.
