  We append two additional black hole (BH) accretion models, namely viscous
disc and gravitational torque-driven accretion, into the Numerical
Investigation of a Hundred Astrophysical Objects (NIHAO) project of galaxy
simulations. We show that these accretion models, characterized by a weaker
dependence on the BH mass compared to the commonly used Bondi-Hoyle accretion,
naturally create a common evolutionary track (co-existence) between the mass of
the BH and the stellar mass of the galaxy, even without any direct coupling via
feedback (FB). While FB is indeed required to control the final BH and stellar
mass of the galaxies, our results suggest that FB might not be the leading
driver of the cosmic co-evolution between these two quantities; in these
models, co-evolution is simply determined by the shared central gas supply.
Conversely, simulations using Bondi-Hoyle accretion show a two-step evolution,
with an early growth of stellar mass followed by exponential growth of the
central supermassive black hole (SMBH). Our results show that the modelling of
BH accretion (sometimes overlooked) is an extremely important part of BH
evolution and can improve our understanding of how scaling relations emerge and
evolve, and whether SMBH and stellar mass co-exist or co-evolve through cosmic
time.
