  In this paper we develop a computationally efficient, two-population,
time-dependent Fokker-Plank approach in the two dimensions of energy and
angular momentum to study the rates of tidal disruption events (TDEs), extreme
mass ratio inspirals (EMRIs) and direct plunges occurring around massive black
holes (MBHs) in galactic nuclei. We test our code by exploring a wide range of
the astrophysically relevant parameter space, including MBH masses, galaxy
central densities and inner density slopes. We find that mass segregation and,
more in general, the time dependency of the distribution function regulate the
event rate: TDEs always decline with time, whereas EMRIs and plunges reach a
maximum and undergo a subsequent nearly exponential decay. Once suitably
normalized, the rates associated to different choices of MBH mass and galaxy
density overlap nearly perfectly. Based on this, we provide a simple scaling
that allows to reproduce the time-dependent event rates for any MBH mass and
underlying galactic nucleus. Although our peak rates are in general agreement
with the literature relying on the steady-state (non-time dependent)
assumption, those can be sustained on a timescale that strongly depends on the
properties of the system. In particular this can be much shorter than a Gyr for
relatively light MBHs residing in dense systems. This warns against using
steady state models to compute global TDE, EMRI and plunge rates and calls for
a more sophisticated, time dependent treatment of the problem.
