  Stars can be ripped apart by tidal forces in the vicinity of a massive black
hole (MBH), causing luminous flares known as tidal disruption events (TDEs).
These events could be contributing to the mass growth of intermediate-mass
MBHs, and new samples from transient surveys can provide useful information on
this growth channel. This work aims to study the demographics of TDEs by
modeling the co-evolution of MBHs and their galactic environments in a
cosmological framework. We use the semi-analytic galaxy formation model
\emph{L-Galaxies}BH, which follows the evolution of galaxies as well as of
MBHs, including multiple scenarios for MBH seeds and growth, spin evolution,
and binary MBH dynamics. Time-dependent TDE rates are associated with each MBH
depending on the stellar environment, following the solutions to the 1-D Fokker
Planck equation solved with \textsc{PhaseFlow}. Our model produces volumetric
rates that are in agreement with the latest optical and previous X-ray samples.
This agreement requires a high occupation fraction of nuclear star clusters
with MBHs since these star reservoirs host the majority of TDEs at all mass
regimes. We predict that TDE rates are an increasing function of MBH mass up to
$\sim\, 10^{5.5}$M$_\odot$, beyond which the distribution flattens and
eventually drops for $>\,10^{7}$M$_\odot$. In general, volumetric rates are
predicted to be redshift-independent at $z\,{<}\,1$. We discuss how the spin
distribution of MBHs around the event horizon suppression can be constrained
via TDE rates and what is the average contribution of TDEs to the MBH growth.
In our work, the majority of low-mass galaxies host nuclear star clusters that
have their loss-cone depleted by $z\,=\,0$, explaining why TDEs are rare in
these systems. This highlights that time-dependent TDE rates are essential for
any model to be in good agreement with observations at all mass regimes.
