  There is mounting evidence that a significant fraction of Black Holes (BHs)
today live in late-type galaxies, including bulge-less galaxies and those
hosting pseudobulges, and are significantly undermassive with respect to the
scaling relations followed by their counterpart BHs in classical bulges of
similar stellar (or even bulge) mass. Here we discuss the predictions of two
state-of-the-art hierarchical galaxy formation models in which BHs grow via
mergers and, in one, also via disk instability. Our aim is to understand if the
wealth of new data on local BH demography is consistent with standard models.
We follow the merger trees of representative subsamples of BHs and compute the
fractional contributions of different processes to the final BH mass. We show
that the model in which BHs always closely follow the growth of their host
bulges, also during late disk instabilities (i.e., bars), produces too narrow a
distribution of BHs at fixed stellar mass to account for the numerous low-mass
BHs now detected in later-type galaxies. Models with a looser connection
between BH growth and bar instability instead predict the existence of a larger
number of undermassive BHs, in better agreement with the observations. The
scatter in the updated local BH-bulge mass relation (with no restriction on
galaxy type) appears to be quite large when including later-type systems, but
it can still be managed to be reproduced within current hierarchical models.
However, the fuelling of BHs during the late bar-instability mode needs to be
better quantified/improved to properly fit the data. We conclude discussing how
the possibly large number of BHs in later type galaxies demands for an in-depth
revision of the local BH mass function and its modelling.
