  We investigate the properties of the most distant quasars
ULASJ134208.10+092838.61 ($z = 7.54$), ULASJ112001.48+064124.3 ($z = 7.08$) and
DELSJ003836.10-152723.6 ($z = 7.02$) studying their Optical-UV emission that
shows clear evidence of the presence of an accretion disk. We model such
emission applying the relativistic disk models KERRBB and SLIMBH for which we
have derived some analytical approximations to describe the observed emission
as a function of the black hole mass, accretion rate, spin and the viewing
angle. We found that: 1] our black hole mass estimates are compatible with the
ones found using the virial argument but with a smaller uncertainty; 2]
assuming that the virial argument is a reliable method to have a black hole
mass measurement (with no systematic uncertainties involved), we found an upper
limit for the black hole spin of the three sources: very high spin values are
ruled out; 3] our Eddington ratio estimates are smaller than those found in
previous studies by a factor $\sim 2$: all sources are found to be
sub-Eddington. Using our results, we explore the parameter space (efficiency,
accretion rate) to describe the possible evolution of the black hole assuming a
$\sim 10^{2-4} M_{\odot}$ seed: if the black hole in these sources formed at
redshift $z = 10 - 20$, we found that the accretion has to proceed at the
Eddington rate with a radiative efficiency $\eta \sim 0.1$ in order to reach
the observed masses in less than $\sim 0.7$ Gyr.
