  In Newtonian gravity the final states of cold dissipationless collapses are
characterized by several structural and dynamical properties remarkably similar
to those of observed elliptical galaxies. Are these properties a peculiarity of
the Newtonian force or a more general feature of long-range forces? We study
this problem by means of $N-$body simulations of dissipationless collapse of
systems of particles interacting via additive $r^{-\alpha}$ forces. We find
that most of the results holding in Newtonian gravity are also valid for
$\alpha\neq2$. In particular the end products are triaxial and never flatter
than an E7 system, their surface density profiles are well described by the
S\'ersic law, the global density slope-anisotropy inequality is obeyed, the
differential energy distribution is an exponential over a large range of
energies (for $\alpha\geq1$), and the pseudo phase-space density is a power law
of radius. In addition, we show that the process of virialization takes longer
(in units of the system's dynamical time) for decreasing values of $\alpha$,
and becomes infinite for $\alpha=-1$ (the harmonic oscillator). This is in
agreement with the results of deep-MOND collapses (qualitatively corresponding
to $\alpha=1$) and it is due to the fact the force becomes more and more
similar to the $\alpha=-1$ case, where as well known no relaxation can happen
and the system oscillates forever.
