- We present K band adaptive optics observations of three high-redshift ( z similar to 2.2) high-luminosity quasars, all of which were studied for the first time. We also observed several point spread function ( PSF) calibrators, non-simultaneously because of the small field of view. The significant temporal PSF variations on timescales of minutes inhibited a straightforward scaled PSF removal from the quasar images. Characterising the degree of PSF concentration by the radii encircling 20% and 80% of the total flux, respectively, we found that even under very different observing conditions the r(20) vs. r(80) relation varied coherently between individual short exposure images, delineating a well-defined relation for point sources. Placing the quasar images on this relation, we see indications that all three objects were resolved. We designed a procedure to estimate the significance of this result, and to estimate host galaxy parameters, by reproducing the statistical distribution of the individual short exposure images. We find in allWe present K band adaptive optics observations of three high-redshift ( z similar to 2.2) high-luminosity quasars, all of which were studied for the first time. We also observed several point spread function ( PSF) calibrators, non-simultaneously because of the small field of view. The significant temporal PSF variations on timescales of minutes inhibited a straightforward scaled PSF removal from the quasar images. Characterising the degree of PSF concentration by the radii encircling 20% and 80% of the total flux, respectively, we found that even under very different observing conditions the r(20) vs. r(80) relation varied coherently between individual short exposure images, delineating a well-defined relation for point sources. Placing the quasar images on this relation, we see indications that all three objects were resolved. We designed a procedure to estimate the significance of this result, and to estimate host galaxy parameters, by reproducing the statistical distribution of the individual short exposure images. We find in all three cases evidence for a luminous host galaxy, with a mean absolute magnitude of M-R = - 27.0 and scale lengths around similar to 4 - 12 kpc. Together with a rough estimate of the central black hole masses obtained from C.. line widths, the location of the objects on the bulge luminosity vs. black hole mass relation is not significantly different from the low-redshift regime, assuming only passive evolution of the host galaxy. Corresponding Eddington luminosities are L-nuc/L-Edd similar to 0.1 - 0.6…
