  We study the large scale geometry of the relative free splitting complex and
the relative complex of free factor systems of the rank $n$ free group $F_n$,
relative to the choice of a free factor system of $F_n$, proving that these
complexes are hyperbolic. Furthermore we present the proof in a general
context, obtaining hyperbolicity of the relative free splitting complex and of
the relative complex of free factor systems of a general group $\Gamma$,
relative to the choice of a free factor system of $\Gamma$. The proof yields
information about coarsely transitive families of quasigeodesics in each of
these complexes, expressed in terms of fold paths of free splittings.
