  Observations of high-redshift quasars frequently promote suggestions of large
black hole masses, whose presence so early in cosmic time is not easily
explicable. I consider the parallel with ultraluminous X-ray sources (ULXs) --
now known to be stellar-mass black hole (and neutron star) binaries apparently
radiating far above their Eddington luminosities $L_{\rm Edd}$. The true
luminosity in ULXs is actually only of order $L_{\rm Edd}$, for {\it
stellar-mass} accretors, but has a very anisotropic (`beamed') component, plus
a near-isotropic component of similar luminosity but much lower specific
intensity. Observers viewing ULXs from within the beam but assuming spherical
symmetry deduce a luminosity $\gg L_{\rm Edd}$. These features appear because
the accretors are fed mass at highly super-Eddington rates, most of it expelled
in high-speed ($v >0.2c$) outflows from the accretion disc.
  I show that in similarly-beamed AGN, emission-line properties would be
essentially the same as in unbeamed sources, but standard virial mass
indicators unusable because velocity widths are dominated by the outflows, not
bound motions about the black holes. In an ensemble of this kind the apparently
most luminous systems are always the most distant, but have the lowest black
hole masses. Interpreting observations of this ensemble without knowing that
they are beamed leads instead to very high black hole mass estimates. The
analogy with ULXs therefore suggests that high-redshift quasars might actually
have central black hole masses which could have grown from stellar values
within the lookback time. I consider how one might test these ideas
observationally.
