We investigate the end state of the gravitational collapse of a null fluid
in higher-dimensional space-times. Both naked singularities and black holes
are shown to be developing as the final outcome of the collapse. The naked
singularity spectrum in a collapsing Vaidya region (4D) gets covered with
the increase in dimensions and hence higher dimensions favor a black hole i
n comparison to a naked singularity. The cosmic censorship conjecture will
be fully respected for a space of infinite dimension.