  In this paper, we study the gravitational collapse in the {\bf k-}essence
emergent gravity using a generalized Vaidya-type metric as a background. We
also analyze the cosmic censorship hypothesis for this system. We show that the
emergent gravity metric resembles closely to the new type of the generalized
Vaidya metrics for null fluid collapse with the {\bf k-}essence emergent mass
function, where we consider the {\bf k-}essence scalar field being a function
solely of the advanced or the retarded time. This new type of {\bf k-}essence
emergent Vaidya metric has satisfied the required energy conditions. The
existence of the locally naked central singularity, the strength and the
strongness of the singularities for the {\bf k-}essence emergent Vaidya metric
are the interesting outcomes of the present work.

General Relativity and Quantum Cosmology;High Energy Physics - Theory