Context : The small ( \leq 135 km mean radius ) satellites of Saturn are closely related to its rings and together they constitute a complex dynamical system where formation and destruction mechanisms compete against each other .
The Cassini-Huygens mission provided high-resolution images of the surfaces of these satellites and therefore allowed for the calculation of observational crater counts .

Aims : 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 .

Methods : 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 .

Results : 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 \sim 10 ^ { 8 } years .
We have also calculated surface ages for the satellites , which indicate ongoing resurfacing processes .

Conclusions :