  We consider the reasons why a cuspy NFW-like profile persistently occurs in
N-body simulations, in contradiction to some astronomical observations. The
routine method of testing the convergence of N-body simulations (in particular,
the negligibility of two-body scattering effect) is to find the conditions
under which the shape of the formed structures is insensitive to numerical
parameters. The results obtained with this approach suggest a surprisingly
minor role of the particle collisions: the central density profile remains
untouched and close to NFW, even if the simulation time significantly exceeds
the collisional relaxation time $\tau_r$. We analyze the test body distribution
in the halo center with help of the Fokker-Planck equation. It turns out that
the Fokker-Planck diffusion transforms any reasonable initial distribution into
NFW-like profile $\rho\propto r^{-1}$ in a time shorter than $\tau_r$. On the
contrary, profile $\rho\propto r^{-1}$ should survive much longer, being a sort
of attractor: the Fokker-Planck diffusion is self-compensated in this case.
Thus the test body scattering may create a stable NFW-like pseudosolution that
can be mixed up with the real convergence. This fact might help to eliminate
the well-known 'cusp vs. core' problem.
