  In this paper we extend the analysis of gravitational collapse of generalised
Vaidya spacetimes to higher dimensions, in the context of the Cosmic Censorship
Conjecture. We present the sufficient conditions on the generalised Vaidya mass
function, that will generate a locally naked singular end state. Our analysis
here generalises all the earlier works on collapsing higher dimensional
generalised Vaidya spacetimes. With specific examples, we show the existence of
classes of mass functions that lead to a naked singularity in four dimensions,
which gets covered on transition to higher dimensions. Hence for these classes
of mass function Cosmic Censorship gets restored in higher dimensions and the
transition to higher dimensions restricts the set of initial data that results
in a naked singularity.
