  Let $\mathbf{E}$ be a flat Lorentzian space of signature $(2, 1)$. A Margulis
space-time is a noncompact complete flat Lorentzian $3$-manifold
$\mathbf{E}/\Gamma$ with a free holonomy group $\Gamma$ of rank $\mathbf{g},
\mathbf{g} \geq 2$. We consider the case when $\Gamma$ contains a parabolic
element. We obtain a characterization of proper $\Gamma$-actions in terms of
Margulis and Drumm-Charette invariants. We show that $\mathbf{E}/\Gamma$ is
homeomorphic to the interior of a compact handlebody of genus $\mathbf{g}$
generalizing our earlier result. Also, we obtain a bordification of the
Margulis space-time with parabolics by adding a real projective surface at
infinity giving us a compactification as a manifold relative to parabolic end
neighborhoods. Our method is to estimate the translational parts of the affine
transformation group and use some $3$-manifold topology.
