  Massive early-type galaxies follow a tight relation between the mass of their
central supermassive black hole ($\rm M_{BH}$) and their stellar mass ($\rm
M_{\star}$). The origin of observed positive outliers from this relation with
extremely high $\rm M_{BH}$ ($> 10^{9} M_{\odot}$) remains unclear. We present
a study of such outliers in the Hydrangea/C-EAGLE cosmological hydrodynamical
simulations, designed to enable the study of high-mass galaxy formation and
evolution in cluster environments. We find 69 $M_{\rm BH}(M_{\star})$ outliers
at $z=0$, defined as those with $ \rm M_{BH} >10^{7} M_{\odot}$ and $\rm
M_{BH}/\rm M_{\star}> 0.01$. This paper focusses on a sample of 5 extreme
outliers, that have been selected based on their $\rm M_{BH}$ and $\rm
M_{\star}$ values, which are comparable to the most recent estimates of
observed positive outliers. This sample of 5 outliers, classified as `Black
hole monster galaxies' (BMGs), was traced back in time to study their origin
and evolution. In agreement with the results of previous simulations for
lower-mass $\rm M_{BH}(\rm M_{\star})$ outliers, we find that these galaxies
became outliers due to a combination of their early formation times and tidal
stripping. For BMGs with $\rm M_{BH} > 10^9 M_{\odot}$, major mergers (with a
stellar mass ratio of $\mu > 0.25$) at early times ($z>2$) precede the rapid
growth of their supermassive BHs. Furthermore, the scatter in the relation
between $\rm M_{BH}$ and stellar velocity dispersion, $\sigma$, correlates
positively with the scatter in [Mg/Fe]($\sigma$). This indicates that the alpha
enhancement of these galaxies, which is closely related to their star formation
history, is related to the growth of their central BHs.
