  We show that the mass-segregation solution for the steady state distribution
of stars around a massive black hole (MBH) has two branches: the known weak
segregation solution (Bahcall & Wolf 1977), and a newly discovered strong
segregation solution, presented here. The nature of the solution depends on the
heavy-to-light stellar mass ratio M_H/M_L and on the unbound population number
ratio N_H/N_L, through the relaxational coupling parameter \Delta=4 N_H M_H^2
/[N_L M_L^2(3+M_H/M_L)]. When the heavy stars are relatively common
(\Delta>>1), they scatter frequently on each other. This efficient
self-coupling leads to weak mass segregation, where the stars form n \propto
r^{-\alpha_M} mass-dependent cusps near the MBH, with indices \alpha_H=7/4 for
the heavy stars and 3/2<\alpha_L<7/4 for the light stars (i.e.
\max(\alpha_H-\alpha_L)~=1/4). However, when the heavy stars are relatively
rare (\Delta<<1), they scatter mostly on light stars, sink to the center by
dynamical friction and settle into a much steeper cusp with 2~<\alpha_H<11/4,
while the light stars form a 3/2<\alpha_L<7/4 cusp, resulting in strong
segregation (i.e. \max(\alpha_H-\alpha_L)~=1). We show that the present-day
mass function of evolved stellar populations (coeval or continuously star
forming) with a universal initial mass function, separate into two distinct
mass scales, ~1 Mo of main sequence and compact dwarfs, and ~10 Mo of stellar
black holes (SBHs), and have \Delta<0.1. We conclude that it is likely that
many relaxed galactic nuclei are strongly segregated. We review indications of
strong segregation in observations of the Galactic Center and in results of
numeric simulations, and briefly list some possible implications of a very high
central concentration of SBHs around a MBH.
