We consider steady-state mass distributions (mass functions) attained at the
nonlinear stage of fragmentation as a result of fragment coalescence. The
influence of the fragment velocity distribution on the mass function is discussed.
The kinetic equations governing the fragments "quasiparticles" are solved using
the group symmetry properties of the collision integral. We have calculated
power indices and locations of the breaking points for the ross spectrum
(luminosity function) associated with the transition from the collisionless
Lynden-Bell type to the Maxwellian distribution, as well as with the
predominance of either purely geometric or Newtonian collision cross sections.
The power indices found are in a reasonable agreement with the values observed
for star or galaxy clusters.