  We associate a contractible ``outer space'' to any free product of groups
G=G_1*...*G_q. It equals Culler-Vogtmann space when G is free,
McCullough-Miller space when no G_i is Z. Our proof of contractibility (given
when G is not free) is based on Skora's idea of deforming morphisms between
trees.
  Using the action of Out(G) on this space, we show that Out(G) has finite
virtual cohomological dimension, or is VFL (it has a finite index subgroup with
a finite classifying space), if the groups G_i and Out(G_i) have similar
properties. We deduce that Out(G) is VFL if G is a torsion-free hyperbolic
group, or a limit group (finitely generated fully residually free group).
