  Let $A_1,...,A_k$ be a system of free factors of $F_n$. The group of relative
automorphisms $Aut(F_n;A_1,...,A_k)$ is the group given by the automorphisms of
$F_n$ that restricted to each $A_i$ are conjugations by elements in $F_n$. The
group of relative outer automorphisms is defined as $Out(F_n;A_1,...,A_k) =
Aut(F_n;A_1,...,A_k)/Inn(F_n)$, where $Inn(F_n)$ is the normal subgroup of
$Aut(F_n)$ given by all the inner automorphisms. We define a contractible space
on which $Out(F_n;A_1,...,A_k)$ acts with finite stabilizers and we compute the
virtual cohomological dimension of this group.
