We investigate possible signatures of a Kerr naked singularity (superspinar) in various observational phenomena. It has been shown that Kerr naked singularities (superspinars) have to be efficiently converted to a black hole due to accretion from Keplerian discs. In the final stages of the conversion process the near-extreme Kerr naked singularities (superspinars) provide a variety of extraordinary physical phenomena. Such superspinning Kerr geometries can serve as an efficient accelerator for extremelyhigh-energy collisions, enabling a direct and clear demonstration of the outcomes of the collision processes. We shall discuss the efficiency and the visibility of the ultra-highenergy collisions in the deepest parts of the gravitational well of superspinning near-extreme Kerr geometries for the whole variety of particles freely falling from infinity. We demonstrate that ultrahigh- energy processes can be obtained with no fine tuning of the motion constants and the products of the colli