  Using the canonical JSJ splitting, we describe the outer automorphism group
$\Out(G)$ of a one-ended word hyperbolic group $G$. In particular, we discuss
to what extent $\Out(G)$ is virtually a direct product of mapping class groups
and a free abelian group, and we determine for which groups $\Out(G)$ is
infinite. We also show that there are only finitely many conjugacy classes of
torsion elements in $\Out(G)$, for $G$ any torsion-free hyperbolic group.
  More generally, let $\Gamma $ be a finite graph of groups decomposition of an
arbitrary group $G$ such that edge groups $G_e$ are rigid (i.e\. $\Out(G_e)$ is
finite). We describe the group of automorphisms of $G$ preserving $\Gamma $, by
comparing it to direct products of suitably defined mapping class groups of
vertex groups.
