  We present results of a deep HST/WFPC2 imaging study of 17 quasars at z~0.4,
designed to determine the properties of their host galaxies. The sample
consists of quasars with absolute magnitudes in the range -24>M_V>-28, allowing
us to investigate host galaxy properties across a decade in quasar luminosity,
but at a single redshift. We find that the hosts of all the RLQs, and all the
RQQs with nuclear luminosities M_V<-24, are massive bulge-dominated galaxies,
confirming and extending the trends deduced from our previous studies. From the
best-fitting model host galaxies we have estimated spheroid and black-hole
masses, and the efficiency (with respect to Eddington luminosity) with which
each quasar is radiating. The largest inferred black-hole mass in our sample is
\~3.10^9 M_sun, comparable to those at the centres of M87 and Cygnus A. We find
no evidence for super-Eddington accretion in even the most luminous objects. We
investigate the role of scatter in the black-hole:spheroid mass relation in
determining the ratio of quasar to host-galaxy luminosity, by generating
simulated populations of quasars lying in hosts with a Schechter mass function.
Within the subsample of the highest luminosity quasars, the observed variation
in nuclear-host luminosity ratio is consistent with being the result of the
scatter in the black-hole:spheroid relation. Quasars with high nuclear-host
ratios can be explained by sub-Eddington accretion onto black holes in the
high-mass tail of the black-hole:spheroid relation. Our results imply that,
owing to the Schechter cutoff, host mass should not continue to increase
linearly with quasar luminosity, at the very highest luminosities. Any quasars
more luminous than M_V=-27 should be found in massive elliptical hosts which at
the present day would have M_V ~ -24.5.
