  We examine the coarse-grained phase-space density profiles of a set of
recent, high-resolution simulations of galaxy-sized Cold Dark Matter (CDM)
halos. Over two and a half decades in radius the phase-space density closely
follows a power-law, $\rho/\sigma^3 \propto r^{-\alpha}$, with $\alpha =
1.875$. This behaviour matches the self-similar solution obtained by
Bertschinger for secondary infall in a uniformly expanding universe. On the
other hand, the density profile corresponding to Bertschinger's solution (a
power-law of slope $r^{2\alpha-6}$) differs significantly from the density
profiles of CDM halos. We show that isotropic mass distributions with power-law
phase-space density profiles form a one-parameter family of structures
controlled by $\kappa$, the ratio of the velocity dispersion to the peak
circular velocity. For $\kappa=\alpha=1.875$ one recovers the power-law
solution $\rho \propto r^{2\alpha-6}$. For $\kappa$ larger than some critical
value, $\kappa_{cr}$, solutions become non-physical, leading to negative
densities near the center. The critical solution, $\kappa =\kappa_{cr}$, has
the narrowest phase-space density distribution compatible with the power-law
phase-space density stratification constraint. Over three decades in radius the
critical solution is indistinguishable from an NFW profile. Our results thus
suggest that the NFW profile is the result of a hierarchical assembly process
that preserves the phase-space stratification of Bertschinger's infall model
but which ``mixes'' the system maximally, perhaps as a result of repeated
merging.
