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While N-body simulations testify for a cuspy profile of the central region ofthe dark matter haloes, observations favor a shallow, cored density profile ofthe central region of, at least, some spiral galaxies and dwarf spheroidals. Weshow that a central profile, very close to the observed one, inevitably formsin the center of dark matter haloes if we make a supposition about a moderateenergy relaxation of the system during the halo formation. If we assume theenergy exchange between dark matter particles during the halo collapse to benot too intensive, the profile is universal: it depends almost not at all onthe properties of the initial perturbation and is very akin, but not identical,to the Einasto profile with small Einasto index $n\sim 0.5$. We estimate thesize of the 'central core' of the distribution, i.e., the extent of the verycentral region with a respectively gentle profile, and show that the cuspformation is unlikely, even if the dark matter is cold. The obtained profile isin a good agreement with observational data for, at least, some types ofgalaxies, but clearly disagrees with N-body simulations.

The galaxy halo formation in the absence of violent relaxation and a universal density profile of the halo center