  To a large class of graphs of groups we associate a C*-algebra universal for
generators and relations. We show that this C*-algebra is stably isomorphic to
the crossed product induced from the action of the fundamental group of the
graph of groups on the boundary of its Bass-Serre tree. We characterise when
this action is minimal, and find a sufficient condition under which it is
locally contractive. In the case of generalised Baumslag-Solitar graphs of
groups (graphs of groups in which every group is infinite cyclic) we also
characterise topological freeness of this action. We are then able to establish
a dichotomy for simple C*-algebras associated to generalised Baumslag-Solitar
graphs of groups: they are either a Kirchberg algebra, or a stable
Bunce-Deddens algebra.
