Galaxies grow alongside their central supermassive black holes (SMBHs),
linked through fueling and feedback. However, the origins and details of this
co-evolution remain unclear and differ significantly amongst modeling
frameworks. Using a suite of semi-analytic models (SAMs), we trace SMBH mass
assembly across
MBH∼106−10,M⊙. We find
significant discrepancies between observations and physics-based models of the
local black hole mass function (BHMF), likely due to differences in the
underlying stellar mass function and the scaling relations therefrom used to
infer the BHMF. However, most physics-based models agree at
z∼1−4 and
align reasonably well with broad-line AGN BHMF from JWST observations at
z=4−5. Most physics-based models reproduce the bolometric AGN luminosity
evolution, except {\sc Dark Sage}, which predicts an excess deviating from
models and observations. Interestingly, this pronounced ``knee' in the
bolometric AGN luminosity function predicted by {\sc Dark Sage} around $L_{\rm
bol} \sim 10^{46} \, \mathrm{erg \, s^{-1}}$ is consistent with the inferred
luminosity of ``Little Red Dots'' at
z=5−6, assuming that their entire
emission originates from AGN activity. We analyze black hole mass build-up and
accretion histories in {\sc Dark Sage}, which, unlike other models, allows for
super-Eddington accretion. We report that on average, SMBHs in {\sc Dark Sage}
primarily grow through secular disk instabilities and merger-driven cold gas
accretion, while black hole mergers contribute 60\% of the total mass budget
only for the most massive SMBHs by
z=0.