Geometric finiteness and uniqueness for Kleinian groups with circle   packing limit sets
  In this paper, we assume that $G$ is a finitely generated torsion free non-elementary Kleinian group with $\Omega(G)$ nonempty. We show that the maximal number of elements of $G$ that can be pinched is precisely the maximal number of rank 1 parabolic subgroups that any group isomorphic to $G$ may contain. A group with this largest number of rank 1 maximal parabolic subgroups is called {\it maximally parabolic}. We show such groups exist. We state our main theorems concisely here.   Theorem I. The limit set of a maximally parabolic group is a circle packing; that is, every component of its regular set is a round disc.   Theorem II. A maximally parabolic group is geometrically finite.   Theorem III. A maximally parabolic pinched function group is determined up to conjugacy in $PSL(2,{\bf C})$ by its abstract isomorphism class and its parabolic elements. 
Linda Keen, Bernard Maskit, Caroline Series