Abstract: 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.