  By performing three-dimensional hydrodynamical simulations of a galaxy in an
isolated dark matter halo, we follow the evolution of the spin parameter $a$ of
a black hole (BH) undergoing super-Eddington phases throughout its growth. This
regime, suspected to be accompanied by powerful jet outflows, is expected to
decrease the BH spin magnitude. We combine super-Eddington accretion with
sub-Eddington phases (quasar and radio modes) and follow the BH spin evolution.
Due to the low frequency of super-Eddington episodes, relativistic jets in this
regime are not able to decrease the magnitude of the spin effectively, as thin
disc accretion in the quasar mode inevitably increases the BH spin. The
combination of super- and sub-Eddington accretion does not lead to a simple
explicit expression for the spin evolution because of feedback from
super-Eddington events. An analytical expression can be used to calculate the
evolution for $a\lesssim0.3$, assuming the super-Eddington feedback is
consistently weak. Finally, BHs starting with low spin magnitude are able to
grow to the highest mass, and if they initially start misaligned with the
galactic disc, they get a small boost of accretion through retrograde
accretion.
