  In this article we carry out a detailed investigation of the geometric nature
of the points at infinity of Minkowski superspace. It turns out that there are
several sets of points forming the superconformal boundary of Minkowski
superspace: on top of a well-behaved super $\mathscr{I}$, we find other sets
that we exhibit and study. We also study the intersection of these boundaries
with super null cones and explicitly construct the corresponding space of super
cuts.
