  We build quasi--isometry invariants of relatively hyperbolic groups which
detect the hyperbolic parts of the group; these are variations of the stable
dimension constructions previously introduced by the authors.
  We prove that, given any finite collection of finitely generated groups
$\mathcal{H}$ each of which either has finite stable dimension or is
non-relatively hyperbolic, there exist infinitely many quasi--isometry types of
one--ended groups which are hyperbolic relative to $\mathcal{H}$.
  The groups are constructed using small cancellation theory over free
products.
