  The phase space corresponding to a particular four-parameter family of
initial data for the gravitational collapse of a spherically symmetric dust
cloud is investigated. In a certain limit of the parameters, this family
reproduces the case of homogenous mass density -constant mass distribution- and
zero initial velocity, while in another limit, it generates a globally naked
singularity. We show that for initial data characterizing flat density
profiles, as well as large initial velocities, the probability of forming a
globally naked singularity is low.
