  We find evidence that crater ejecta play an important role in the small
crater populations on the Saturnian satellites, and more broadly, on cratered
surfaces throughout the Solar System. We measure crater populations in Cassini
images of Enceladus, Rhea, and Mimas, focusing on image data with scales less
than 500 m/pixel. We use recent updates to crater scaling laws and their
constants to estimate the amount of mass ejected in three different velocity
ranges: (i) greater than escape velocity, (ii) less than escape velocity and
faster than the minimum velocity required to make a secondary crater (v_min),
and (iii) velocities less than v_min. Although the vast majority of mass on
each satellite is ejected at speeds less than v_min, our calculations
demonstrate that the differences in mass available in the other two categories
should lead to observable differences in the small crater populations; the
predictions are borne out by the measurements we have made to date. Rhea,
Tethys, and Dione have sufficient surface gravities to retain ejecta moving
fast enough to make secondary crater populations. The smaller satellites, such
as Enceladus but especially Mimas, are expected to have little or no
traditional secondary populations because their escape velocities are near the
threshold velocity necessary to make a secondary crater. Our work clarifies why
the Galilean satellites have extensive secondary crater populations relative to
the Saturnian satellites. The presence, extent, and sizes of sesquinary craters
(craters formed by ejecta that escape into temporary orbits around Saturn
before re-impacting the surface) is not yet well understood. Finally, our work
provides further evidence for a "shallow" size-frequency distribution (slope
index of ~2 for a differential power-law) for comets a few km diameter and
smaller. [slightly abbreviated]
