  We investigate the distribution of orbits of a non-elementary discrete
hyperbolic group acting on the n-dimensional hyperbolic space and its geometric
boundary. In particular, we show that if the group $\Gamma$ admits a finite
Bowen-Margulis-Sullivan measure (for instance, if it is geometrically finite),
then every $\Gamma$-orbit in the hyperbolic space is equidistributed with
respect to the Patterson-Sullivan measure supported on the limit set of
$\Gamma$.The appendix by Maucourant is the extension of a part of his thesis
where he obtains the same result as a simple application of Roblin's theorem.
Our approach is via establishing the equidistribution of solvable flows on the
unit tangent bundle of the quotient manifold, which is of independent interest.
