  Observations of $z \gtrsim 6$ quasars provide information on the early
evolution of the most massive black holes (MBHs) and galaxies. Current
observations, able to trace both gas and stellar properties, reveal a
population of MBHs that is significantly more massive than expected from the
local MBH-stellar mass relation. The population lies on, but mostly above, the
relation observed in the nearby Universe. This suggests that these objects grew
very rapidly. To explain their presence when the Universe was less than 1~Gyr
old and to assess the physical conditions for their rapid growth, we explored
whether episodes of accretion above the Eddington limit can occur across cosmic
epochs. By employing state-of-the-art high-resolution cosmological zoom-in
simulations of a $z\sim 7$ quasar, where different accretion regimes are
included consistently, together with their associated radiative and kinetic
feedback, we show that super-Eddington phases can be sustained for relatively
long timescales (tens of millions of years). This allows the MBH to rapidly
grow by up to three orders of magnitude, depending on the strength of the
kinetic feedback. We also show by means of a semianalytic calculation that the
MBH spin remains moderate and does not take on extremely high values during the
super-Eddington phases. This results in a lower feedback efficiency, which may
allow the rapid growth required to explain over-massive high-redshift MBHs.
