  This paper aims at quantifying discreetness effects, born of finite particle
number, on the dynamics of dark matter haloes forming in the context of
cosmological simulations. By generalising the standard calculation of two body
relaxation to the case when the size and mass distribution are variable, and
parametrising the time evolution using established empirical relations, we find
that the dynamics of a million particle halo is noise-dominated within the
inner percent of the final virial radius. Far larger particle numbers (~ 10^8)
are required for the RMS perturbations to the velocity to drop to the 10 %
level there. The radial scaling of the relaxation time is simple and strong:
t_relax ~ r^2, implying that numbers >> 10^8 are required to faithfully model
the very inner regions; artificial relaxation may thus constitute an important
factor, contributing to the contradictory claims concerning the persistence of
a power law density cusp to the very centre. The cores of substructure haloes
can be many relaxation times old. Since relaxation first causes their expansion
before recontraction occurs, it may render them either more difficult or easier
to disrupt, depending on their orbital parameters. It may thus modify the
characteristics of the subhalo distribution and effects of interactions with
the parent. We derive simple closed form formulas for the characteristic
relaxation times, as well as for the weak N-scaling reported by Diemand et al.
when the main contribution comes from relaxing subhaloes (abridged).
