  Using the general formalism for spherical gravitational collapse developed in
[1], we investigate here the final fate of a spherical distribution of a matter
cloud, where radial pressures vanish but tangential pressures are non-zero.
Within this framework, firstly we examine the effect of introducing a generic
small pressure in a well-known black hole formation process, which is that of
an otherwise pressure-free dust cloud. The intriguing result we find is that a
dust collapse that was going to a black hole final state could now go to a
naked singularity final configuration, when arbitrarily small tangential
pressures are introduced. The implications of such a scenario are discussed in
some detail. Secondly, the approach here allows us to generalize the earlier
results obtained on gravitational collapse with non-zero tangential pressure,
in the presence of a non-zero cosmological constant. Finally, we discuss the
genericity of black hole and naked singularity formation in collapse with
non-zero tangential pressure. The treatment here gives a unified and complete
picture on collapse final states, in terms of black hole and naked singularity
formation, generalizing the earlier results obtained for this class of collapse
models. Thus the role of tangential stresses towards determining collapse
endstates emerges in a straightforward and transparent manner in our treatment.
