[abridged] Quasars (QSOs) at the highest known redshift (z~6) are unique probes of the early growth of supermassive black holes (BHs). Until now, only the most luminous QSOs have been studied, often one object at a time. Here we present the most extensive consistent analysis to date of z>4 QSOs with observed NIR spectra, combining three new z~6 objects from our ongoing VLT-ISAAC program with nineteen 4<z<6.5 sources from the literature. The new sources extend the existing SDSS sample towards the faint end of the QSO luminosity function. Using a maximum likelihood fitting routine optimized for our spectral decomposition, we estimate the black hole mass (MBH), the Eddington ratio (defined as Lbol/LEdd) and the FeII/MgII line ratio, a proxy for the chemical abundance, to characterize both the central object and the broad line region gas. The QSOs in our sample host BHs with masses of ~10^9 Modot that are accreting close to the Eddington luminosity, consistent with earlier results. We find that the distribution of observed Eddington ratios is significantly different than that of a luminosity-matched comparison sample of SDSS QSOs at lower redshift (0.35<z<2.25): the average <log(Lbol/LEdd)>=-0.37 (Lbol/LEdd~0.43) with a scatter of 0.20 dex for the z>4 sample and the <log(Lbol/LEdd)>=-0.80 (Lbol/LEdd~0.16) with a scatter of 0.24 dex for the 0.35<z<2.25 sample. This implies that, at a given luminosity, the MBH at high-z is typically lower than the average MBH of the lower-redshift population, i.e. the z>4 sources are accreting significantly faster than the lower-redshift ones. We show that the derived FeII/MgII ratios depend sensitively on the performed analysis: our self-consistent, homogeneous analysis significantly reduces the FeII/MgII scatter found in previous studies. The measured FeII/MgII line ratios show no sign of evolution with cosmic time in the redshift range 4<z<6.5 [...]
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