Numerical simulations of the accretion process in Kerr spacetimes with arbitrary value of the Kerr parameter

According to the Cosmic Censorship Conjecture, all the singularities produced by the collapsing matter must be hidden behind an event horizon. In 4D general relativity, this implies that the final product of the collapse is a Kerr-Newman black hole. Here I consider the possibility that the Cosmic Censorship Conjecture can be violated. I present the results of some numerical simulations of the accretion process onto Kerr black holes (objects with event horizon) and Kerr super-spinars (fast-rotating objects without event horizon). This is a preliminary study to investigate how the Cosmic Censorship Conjecture can be tested by astrophysical observations.