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Abstract We present measurements of black hole masses and Eddington ratios (λ_Edd) for a sample of 38 bright (M₁₄₅₀< −24.4 mag) quasars at 5.8 ≲z≲ 7.5, derived from Very Large Telescope/X–shooter near–IR spectroscopy of their broad Civand Mgiiemission lines. The black hole masses (on average,M_BH∼ 4.6 × 10⁹M_⊙) and accretion rates (0.1 ≲λ_Edd≲ 1.0) are broadly consistent with that of similarly luminous 0.3 ≲z≲ 2.3 quasars, but there is evidence for a mild increase in the Eddington ratio abovez≳ 6. Combined with deep Atacama Large Millimeter/submillimeter Array (ALMA) observations of the [CII] 158μm line from the host galaxies and VLT/MUSE investigations of the extended Lyαhalos, this study provides fundamental clues to models of the formation and growth of the first massive galaxies and black holes. Compared to local scaling relations,z≳ 5.7 black holes appear to be over-massive relative to their hosts, with accretion properties that do not change with host galaxy morphologies. Assuming that the kinematics of theT∼ 10⁴K gas, traced by the extended Lyαhalos, are dominated by the gravitational potential of the dark matter halo, we observe a similar relation between black hole mass and circular velocity as reported forz∼ 0 galaxies. These results paint a picture where the first supermassive black holes reside in massive halos atz≳ 6 and lead the first stages of galaxy formation by rapidly growing in mass with a duty cycle of order unity. The duty cycle needs to drastically drop toward lower redshifts, while the host galaxies continue forming stars at a rate of hundreds of solar masses per year, sustained by the large reservoirs of cool gas surrounding them.