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We study the Resonant Relaxation (RR) of an axisymmetric low mass (orKeplerian) stellar disc orbiting a more massive black hole (MBH). Our recentwork on the general kinetic theory of RR is simplified in the standard mannerby ignoring the effects of `gravitational polarization', and applied to azero-thickness, flat, axisymmetric disc. The wake of a stellar orbit isexpressed in terms of the angular momenta exchanged with other orbits, and usedto derive a kinetic equation for RR under the combined actions of self-gravity,1 PN and 1.5 PN relativistic effects of the MBH and an arbitrary externalaxisymmetric potential. This is a Fokker-Planck equation for the stellardistribution function (DF), wherein the diffusion coefficients are givenself-consistently in terms of contributions from apsidal resonances betweenpairs of stellar orbits. The physical kinetics is studied for the two maincases of interest. (1) `Lossless' discs in which the MBH is not a sink ofstars, and disc mass, angular momentum and energy are conserved: we prove thatgeneral H-functions can increase or decrease during RR, but the Boltzmannentropy is (essentially) unique in being a non-decreasing function of time.Therefore secular thermal equilibria are maximum entropy states, with DFs ofthe Boltzmann form; the two-Ring correlation function at equilibrium iscomputed. (2) Discs that lose stars to the MBH through an `empty loss-cone': wederive expressions for the MBH feeding rates of mass, angular momentum andenergy in terms of the diffusive flux at the loss-cone boundary.

Stellar Dynamics around a Massive Black Hole III: Resonant Relaxation of Axisymmetric Discs