  Stars can be either disrupted as tidal disruption events (TDEs) or swallowed
as a whole by massive black holes (MBHs) at galactic centers when they approach
sufficiently close to these MBHs. In this work, we investigate the correlations
of such stellar consumption rates with both the MBH mass $M_{\rm bh}$ and the
inner slope of the host galaxy mass density distribution $\alpha$. We introduce
a simplified analytical power-law model with a power-law stellar mass density
distribution surrounding MBHs and separate the contributions of two-body
relaxation and stellar orbital precession for the stellar orbital angular
momentum evolution in nonspherical galaxy potentials. The stellar consumption
rates derived from this simplified model can be well consistent with the
numerical results obtained with a more realistic treatment of stellar
distributions and dynamics around MBHs, providing an efficient way to estimate
TDE rates. The origin of the correlations of stellar consumption rates with
$M_{\rm bh}$ and $\alpha$ are explained by the dependence of this analytical
model on those MBH/host galaxy properties and by the separation of the stellar
angular momentum evolution mechanisms. We propose that the strong positive
correlation between the rates of stellar consumption due to two-body relaxation
and $\alpha$ provides one interpretation for the overrepresentation of TDEs
found in some rare E+A/poststarburst galaxies. We find high TDE rates for giant
stars, up to those for solar-type stars. The understanding of the origin of the
correlations of the stellar consumption rates will be necessary for obtaining
the demographics of MBHs and their host galaxies via TDEs.
