  Gravitational torques among objects orbiting a supermassive black hole drive
the rapid reorientation of orbital planes in nuclear star clusters (NSCs), a
process known as vector resonant relaxation. In this Letter, we determine the
statistical equilibrium of systems with a distribution of masses, semimajor
axes, and eccentricities. We average the interaction over the apsidal
precession time and construct a Monte Carlo Markov chain method to sample the
microcanonical ensemble of the NSC. We examine the case of NSCs formed by 16
episodes of star formation or globular cluster infall. We find that the massive
stars and stellar mass black holes form a warped disk, while low mass stars
resemble a spherical distribution with a possible net rotation. This explains
the origin of the clockwise disk in the Galactic center and predicts a
population of black holes (BHs) embedded within this structure. The rate of
mergers among massive stars, tidal disruption events of massive stars by BHs,
and BH-BH mergers are highly increased in such disks. The first two may explain
the origin of the observed G1 and G2 clouds, the latter may be important for
gravitational wave detections with LIGO and VIRGO. More generally, black holes
are expected to settle in disks in all dense spherical stellar systems
assembled by mergers of smaller systems including globular clusters.
