  We study the geometry and dynamics of discrete subgroups $\Gamma$ of
$\PSL(3,\mathbb{C})$ with an open invariant set $\Omega \subset \PC^2$ where
the action is properly discontinuous and the quotient $\Omega/\Gamma$ contains
a connected component whicis compact. We call such groups {\it
quasi-cocompact}. In this case $\Omega/\Gamma$ is a compact complex projective
orbifold and $\Omega$ is a {\it divisible set}. Our first theorem refines
classical work by Kobayashi-Ochiai and others about complex surfaces with a
projective structure: We prove that every such group is either virtually affine
or complex hyperbolic. We then classify the divisible sets that appear in this
way, the corresponding quasi-cocompact groups and the orbifolds
$\Omega/\Gamma$. We also prove that excluding a few exceptional cases, the
Kulkarni region of discontinuity coincides with the equicontinuity region and
is the largest open invariant set where the action is properly discontinuous.
