  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.
