The discovery of a relationship between the central black hole and the properties of their host galaxies is a fundamental ingredient for a comprehensive interpretation of the structure and evolution of the galaxies. Of particular relevance is the understanding how this relationship evolves over the cosmic time and can offer important clues for the study of the formation processes of galaxies and their central massive BHs. To investigate this issue we need to measure the black hole mass and the properties (luminosity, size, morphology, stellar population, …) of a suitable sample of active galaxies at different redshift. This requires exceptional observing capabilities in terms of sensitivity and spatial resolution. In order to explore this link it is needed to measure both the mass of the central BH and the properties of its host galaxy over a significant cosmic time. This can be done using spatially resolved spectroscopy of quasars and their host galaxies. The BH mass can be derived from the width of the broad emission lines and the continuum luminosity of the nucleus (using virial method from single epoch spectra or more accurately getting the size of BLR from reverberation mapping technique). At z > 2 quasar host galaxies are angularly very small (0.2”-0.3” half light radius) therefore it is extremely important to image the sources with a very narrow PSF (to reduce the emission from the nucleus) and high sensitivity to properly detect the faint extended emission from the galaxies.
Here is a list of studies on the properties of QSO host galaxies
Adaptive optics imaging of high luminosity quasars. -- 2016 AJ 2016AJ....152...38L (PDF)
Low redshift quasars in the Stripe82: The host galaxies -- 2014 MNRAS 440, 476 (PDF)
The low-mass end of the MBH / Mhost relation in quasars -- 2012 Advances in Astronomy, id. 782528 (PDF)
The quasar M_bh - M_host relation through Cosmic Time II -- 2010 MNRAS 402 2453 (PDF)
The quasar M_bh - M_host relation through Cosmic Time I -- 2009 MNRAS 402 2441 (PDF)
The properties of quasar hosts at the peak of the quasar activity. 2009, ApJ 703 1663
Downsizing of supermassive black holes from the SDSS quasar survey 2009MNRAS.396.1537L
Near infrared adaptive optics imaging of high redshift quasars. 2008 ApJ 673 694
The nuclear to host galaxy relation of high redshift quasars 2007 ApJ 660 1039
The host galaxies of radio-quiet quasars at 0.5< z <1.0 2007A&A 462..525
VLT adaptive optics imaging of QSO host galaxies and their close environment at z ∼ 2.5. 2005 A&A 434, 469
The cosmic evolution of quasar host galaxies 2004, ApJ 604 495
Host galaxies of low z radio loud quasars: 2003 ApJ, 596 830
Near-infrared imaging of the host galaxies of three radio-loud quasars at z = 1.5 2001, ApJ 547, 124
Near-IR imaging of the host galaxies of moderate redshift steep spectrum radio quasars.2000 AA 364 70.
Near--infrared imaging of the host galaxies of flat spectrum radio quasar 1998 A&A 332, 503