  Mass and spin are the only two parameters needed to completely characterize
black holes in General Relativity. However, the interaction between black holes
and their environment is where complexity lies, as the relevant physical
processes occur over a large range of scales. That is particularly relevant in
the case of super-massive black holes (SMBHs), hosted in galaxy centers, and
surrounded by swirling gas and various generations of stars. These compete with
the SMBH for gas consumption and affect both dynamics and thermodynamics of the
gas itself. How the behavior of such fiery environment influence the angular
momentum of the gas accreted onto SMBHs, and, hence, black-hole spins is
uncertain. We explore the interaction between SMBHs and their environment via
first 3D sub-parsec resolution simulations (ranging from 0.1 pc to 1 kpc
scales) that study the evolution of the SMBH spin by including the effects of
star formation, stellar feedback, radiative transfer, and metal pollution
according to the proper stellar yields and lifetimes. This approach is crucial
to investigate the impact of star formation processes and feedback effects on
the angular momentum of the material that could accrete on the central hole. We
find that star formation and feedback mechanisms can locally inject significant
amounts of entropy in the surrounding medium, and impact on the inflow
inclination angles and Eddington fractions. As a consequence, the resulting
trends show upper-intermediate equilibrium values for the spin parameter, a, of
about 0.6 - 0.9, corresponding to radiative efficiencies \epsilon = 9% - 15%.
These results suggest that star formation feedback taking place in the
circum-nuclear disk during the in-fall cannot induce alone very strong chaotic
trends in the gas flow, quite independently from the different numerical
parameters.
