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Observations of $z \gtrsim 6$ quasars provide information on the early phasesof the most massive black holes (MBHs) and galaxies. Current observations, ableto trace both gas and stellar properties, show that most MBHs at high redshiftseem overmassive compared to the local population, in line with the ellipticalgalaxy population, or even above, thus implying a very rapid growth of theseobjects. To assess the physical conditions for such a rapid growth and explainthe existence of a population of already mature MBHs when the Universe was lessthan 1~Gyr old, we here explore whether episodes of accretion above theEddington limit can occur across cosmic epochs. By employing state-of-the-arthigh-resolution cosmological zoom-in simulations of a $z\sim 7$ quasar, wheredifferent accretion regimes are consistently included, together with theirassociated radiative and kinetic feedback, we show that super-Eddington phasescan be sustained for relatively long time-scales (tens of Myr) and discuss howthey affect the growth of MBHs. We also show, by means of a semi-analyticevolution, that the MBH spin remains relatively low during super-Eddingtonphases, and this would result in a lower feedback efficiency, hence apotentially faster growth that might then explain the overmassiveness ofhigh-redshift MBHs.

Sustained super-Eddington accretion in high-redshift quasars