  The paper consists of two parts. In the first one we show that a relatively
hyperbolic group $G$ splits as a star graph of groups whose central vertex
group is finitely generated and the other vertex groups are maximal parabolic
subgroups. As a corollary we obtain that every group which admits
3-discontinuous and 2-cocompact action by homeomorphisms on a compactum is
finitely generated with respect to a system of parabolic subgroups.
  The second part essentially uses the methods of topological entourages
developed in the first part. Using also Floyd metrics we obtain finer
properties of finitely generated relatively hyperbolic groups. We show that
there is a system of "tight" curves satisfying the property of horospherical
quasiconvexity. We then prove that the Floyd quasigeodesics are tight and so
the parabolic subgroups of $G$ are quasiconvex with respect to the Floyd
metrics. As a corollary we obtain that the preimage of a parabolic point by the
Floyd map is the Floyd boundary of its stabilizer.
