  We analyze here the final fate of complete gravitational collapse of a
massless scalar field within general relativity. A class of dynamical solutions
with initial data close to the Friedmann-Lemaitre-Robertson-Walker (FLRW)
collapse model is explicitly given and the Einstein equations are integrated
numerically in a neighborhood of the center. We show that the initial data
space is evenly divided between the dynamical evolutions that terminate in a
black hole final state and those that produce a locally naked singularity. We
comment on the genericity aspects of the collapse end-states and the connection
to cosmic censorship conjecture is pointed out.
