Gravitational lensing assists in the detection of quasar hosts by amplifying and distorting the host light away from the unresolved quasar core images .
We present the results of HST observations of 30 quasar hosts at redshifts 1 < z < 4.5 .
The hosts are small in size ( r _ { e } \lesssim 6 kpc ) , and span a range of morphologies consistent with early-types ( though smaller in mass ) to disky/late-type .
The ratio of the black hole mass ( M _ { BH } , from the virial technique ) to the bulge mass ( M _ { bulge } , from the stellar luminosity ) at 1 \lesssim z \lesssim 1.7 is broadly consistent with the local value ; while M _ { BH } / M _ { bulge } at z \gtrsim 1.7 is a factor of 3–6 higher than the local value .
But , depending on the stellar content the ratio may decline at z \gtrsim 4 ( if E/S0-like ) , flatten off to 6–10 times the local value ( if Sbc-like ) , or continue to rise ( if Im-like ) .
We infer that galaxy bulge masses must have grown by a factor of 3–6 over the redshift range 3 \gtrsim z \gtrsim 1 , and then changed little since z \sim 1 .
This suggests that the peak epoch of galaxy formation for massive galaxies is above z \sim 1 .
We also estimate the duty cycle of luminous AGNs at z \gtrsim 1 to be \sim 1 \% , or 10 ^ { 7 } yrs , with sizable scatter .