  The small ($\le$ 135 km mean radius) saturnian satellites are closely related
to the rings and together they constitute a complex dynamical system where
formation and destruction mechanisms compete against each other. We model the
cratering process by Centaur objects on the small saturnian satellites, and
compare our results with the observational crater counts obtained from the
Voyager and Cassini missions. Using a theoretical model previously developed we
calculate the crater production on these satellites considering two slopes of
the size-frequency distribution (SFD) for the smaller objects of the Centaur
population and compare our results with the available observations. In
addition, we consider the case of catastrophic collisions between these
satellites and Centaur objects and calculate the age of formation of those
satellites that suffer one or more disruptions. In general we find that the
observed crater distributions are best modeled by the crater size distribution
corresponding to the $s_2 = 3.5$ index of the SFD of impactors with diameters
smaller than 60 km. However, for crater diameters $D \lesssim 3-8$ km (which
correspond to impactor diameters $d \sim 0.04 - 0.15$ km), the observed
distributions become flatter and deviate from our results, which may evidence
processes of erosion and/or crater saturation at small crater sizes or a
possible break in the SFD of impactors at $d \sim 0.04 - 0.15$ km to a much
shallower differential slope of $\sim -1.5$. Our results suggest that Pan,
Daphnis, Atlas, Aegaeon, Methone, Anthe, Pallene, Calypso and Polydeuces
suffered one or more catastrophic collisions over the age of the Solar System,
the younger being associated to arcs with ages of $\sim10^8$ years. We have
also calculated the satellites' surface ages, which indicate ongoing
resurfacing processes.
