very steep within $\Re$, while MOND and dMOND profiles are significantly flatter there. As well as $\sigma_r$, $\sglos$ decreases for decreasing radius in the inner region of model D. The kinematical properties of M2 and M4 are intermediate between those of M1 and of N: overall we find only weak dynamical non-homology among MOND end-products. The empty symbols in Fig. \[fig3d\] (right column) refer to a test Newtonian simulation run with the FVFPS treecode (with $4\times10^5$ particles). The structural and kinematical properties of the end-product of this simulation are clearly in good agreement with those of the end-product of simulation N (solid lines), which started from the same initial conditions.

Phase-space properties of MOND collapses {#secphsp}
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To explore the phase-space evolution of the systems during the collapse and the following relaxation we consider time snapshots of the particles radial velocity ($\vr$) vs. radius as in Londrillo et al. (1991). In Fig. \[figphsp\] we plot five of these diagrams for simulations D, M1 and N: each plot shows the phase-space coordinates of 32000 particles randomly extracted from the corresponding simulation, and, as in Fig. \[figtime\], times are normalized to the dynamical time ${t_{\rm dyn}}$ (see Section \[secic\]). At time $t=0.5{t_{\rm 