We present the results of a deep HST/WFPC2 imaging study of 17 quasars at z \simeq 0.4 , designed to determine the properties of their host galaxies .
The sample consists of quasars with absolute magnitudes in the range -24 \geq M _ { V } \geq - 28 , allowing us to investigate host galaxy properties across a decade in quasar luminosity , but at a single redshift .
Our previous imaging studies of AGN hosts have focussed primarily on quasars of moderate luminosity , but the most powerful objects in the current sample have powers comparable to the most luminous quasars found at high redshifts .

We find that the host galaxies of all the radio-loud quasars , and all the radio-quiet quasars in our sample 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 hence black-hole masses , and the efficiency ( with respect to the Eddington luminosity ) with which each quasar is emitting radiation .
The largest inferred black-hole mass in our sample is M _ { BH } \simeq 3 \times 10 ^ { 9 } { M _ { \odot } } , comparable to the mass of the black-holes at the centres of M87 and Cygnus A .
We find no evidence for super-Eddington accretion rates in even the most luminous objects ( 0.05 < L / L _ { Edd } < 1.0 ) .

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 luminosity ratios can be explained in terms of sub-Eddington accretion rates onto black-holes in the high-mass tail of the black-hole : spheroid relation .
Our results imply that , owing to the Schechter function 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 } \simeq - 24.5 .