We compare and contrast recent results we have published on a finite system of isothermal self-gravitating particles with the one obtained by Zel'dovich and Podurets.

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We investigate the stability of dense stellar clusters against relativistic collapse by approximate methods described in the previous paper in this series. These methods, together with the analysis of the fractional binding energy of the system, have been applied to sequences of equilibrium models, with cuto † in the distribution function, which generalize those studied by Zeldovich & Podurets. We show the existence of extreme conÐgurations, which are stable all the way up to inÐnite values of the central redshift.

We examine the Newtonian equilibrium configurations of a system of bosons undergoing quantum condensation, with a distribution function with a cutoff in the momentum space. Bounded configurations with a core of condensed particles surrounded by an uncondensed phase are obtained. The results are compared and contrasted with the ones in which the spatial divergences are removed by a cut-off in density. The well-known solution corresponding to fully condensed configurations is obtained for suitable values of the central density.