[en] Direct numerical integrations of the two-dimensional Fokker–Planck equation are carried out for compact objects orbiting a supermassive black hole at the center of a galaxy. As in Papers I–III, the diffusion coefficients incorporate the effects of the lowest-order post-Newtonian corrections to the equations of motion. In addition, terms describing the loss of orbital energy and angular momentum due to the 5/2-order post-Newtonian terms are included. In the steady state, captures are found to occur in two regimes that are clearly differentiated in terms of energy, or semimajor axis; these two regimes are naturally characterized as “plunges” (low binding energy) and “EMRIs,” or extreme-mass-ratio inspirals (high binding energy). The capture rate, and the distribution of orbital elements of the captured objects, are presented for two steady-state models based on the Milky Way: one with a relatively high density of remnants and one with a lower density. In both models, but particularly in the second, the steady-state $\stackrel{¯<!--\; ??\; -->}{f}(E)$ and the distribution of orbital elements of the captured objects are substantially different than if the Bahcall–Wolf energy distribution were assumed. The ability of classical relaxation to soften the blocking effects of the Schwarzschild barrier is quantified. These results, together with those of Papers I–III, suggest that a Fokker–Planck description can adequately represent the dynamics of collisional loss cones in the relativistic regime.