  We argue that a universal density profile for dark matter halos arises as a
natural consequence of hierarchical structure formation. It is a fixed point in
the process of repeated mergers. We present analytic and numerical arguments
for the emergence of a particular form of the profile. At small radii, the
density should vary as $r^{-\alpha}$, with $\alpha$ determined by the way the
characteristic density of halos scales with their mass. If small halos are
dense, then $\alpha$ is large. The mass-density relation can be related to the
power spectrum of initial fluctuations, $P(k)$, through `formation time'
arguments. Early structure formation leads to steep cusps. For $P(k)\sim k^n$
we find $\alpha\simeq 3(3+n)/(5+n)$. The universal profile is generated by
tidal stripping of small halos as they merge with larger objects.
