  Relaxed dark-matter haloes are found to exhibit the same universal density
profiles regardless of whether they form in hierarchical cosmologies or via
spherical collapse. Likewise, the shape parameters of haloes formed
hierarchically do not seem to depend on the epoch in which the last major
merger took place. Both findings suggest that the density profile of haloes
does not depend on their aggregation history. Yet, this possibility is
apparently at odds with some correlations involving the scale radius r_s found
in numerical simulations. Here we prove that the scale radius of relaxed,
non-rotating, spherically symmetric haloes endowed with the universal density
profile is determined exclusively by the current values of four independent,
though correlated, quantities: mass, energy and their respective instantaneous
accretion rates. Under this premise and taking into account the inside-out
growth of haloes during the accretion phase between major mergers, we build a
simple physical model for the evolution of r_s along the main branch of halo
merger trees that reproduces all the empirical trends shown by this parameter
in N-body simulations. This confirms the conclusion that the empirical
correlations involving r_s do not actually imply the dependence of this
parameter on the halo aggregation history. The present results give strong
support to the explanation put forward in a recent paper by Manrique et al.
(2003) for the origin of the halo universal density profile.
