Bounded geometry in relatively hyperbolic groups
  We prove that, if a group is relatively hyperbolic, the parabolic subgroups are virtually nilpotent if and only if there exists a hyperbolic space with bounded geometry on which it acts geometrically finitely.   This provides, by use of M. Bonk and O. Schramm embedding theorem, a very short proof of the finiteness of asymptotic dimension of relatively hyperbolic groups with virtually nilpotent parabolic subgroups (which is known to imply Novikov conjectures 
F. Dahmani, A. Yaman