In order to understand of halo structures we focused in obtaining a systematic understanding of the quasi-stationary properties of the mass distributions resulting from the gravitational evolution of isolated systems. To this aim we considered
controlled numerical experiments in which a system is prepared in a relatively simple initial condition, and it then evolves numerically through gravitational dynamics. In this way we were able to understand the mass and energy ejection in cold collapses {\bf [63]} the difference between warm and cold collaspes {\bf [74]}, the origin of the universal properties of QSS from cold collapses {\bf [75]}, the effect of symmetry breaking {\bf [80]}, the generation of trixiality {\bf [81]}, and of angular momentum {\bf [82]}, the formation of satellites {\bf [83]}, the effects of discreteness {\bf [85]} and the difference between the properties of QSS generated from a top-down and a bottom-up dynamics {\bf [95]}. In addition we studied the case in which the initial  systems breaks spherical symmetry and has some angular momentum and  we showed that in such collision-less dynamics, quite generally, there are formed long-lived transient out-of-equilibrium structures with a rich variety of shapes such as spiral arms with or without bars and/or rings, that can have significant observational signatures and consequences {\bf [86,89]}.