  We present the results of a deep K-band imaging study which reveals the host
galaxies around a sample of luminous radio-quiet quasars. The K-band images,
obtained at UKIRT, are of sufficient quality to allow accurate modelling of the
underlying host galaxy. Initially, the basic structure of the hosts is revealed
using a modified Clean deconvolution routine optimised for this analysis. 2 of
the 14 quasars are shown to have host galaxies with violently disturbed
morphologies which cannot be modelled by smooth elliptical profiles. For the
remainder of our sample, 2D models of the host and nuclear component are fitted
to the images using the chi-squared statistic to determine goodness of fit.
Host galaxies are detected around all of the quasars. The reliability of the
modelling is extensively tested, and we find the host luminosity to be well
constrained for 9 quasars. The derived average K-band absolute K-corrected host
galaxy magnitude for these luminous radio-quiet quasars is <M_K>=-25.15+/-0.04,
slightly more luminous than an L* galaxy. The spread of derived host galaxy
luminosities is small, although the spread of nuclear-to-host ratios is not.
These host luminosities are shown to be comparable to those derived from
samples of quasars of lower total luminosity and we conclude that there is no
correlation between host and nuclear luminosity for these quasars.
Nuclear-to-host ratios break the lower limit previously suggested from studies
of lower nuclear luminosity quasars and Seyfert galaxies. Morphologies are less
certain but, on the scales probed by these images, some hosts appear to be
dominated by spheroids but others appear to have disk-dominated profiles.
