  Non-static, spherically symmetric clusters of counter-rotating particles, of
the type first introduced by Einstein, are analysed here. The initial data
space can be parameterized in terms of three arbitrary functions, namely;
initial density, velocity and angular momentum profiles. The final state of
collapse, black hole or naked singularity, turns out to depend on the order of
the first non-vanishing derivatives of such functions at the centre. The work
extends recent results by Harada, Iguchi and Nakao.
