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Sources at the brightest end of QSO luminosity function during the peak epochof star formation and black hole accretion (z~2-4, i.e. Cosmic noon) areprivileged sites to study the feeding & feedback cycle of massive galaxies. Weperform the first systematic study of cold gas properties in the most luminousQSOs, by characterising their host-galaxies and environment. We analyse ALMA,NOEMA and JVLA observations of FIR continuum, CO and [CII] emission lines ineight QSOs ($L_{\rm Bol}>3\times10^{47}$ erg/s) from the WISSH sample atz~2.4-4.7. We report a 100% emission line detection rate and a 80% detectionrate in continuum emission, and we find CO emission to be consistent with thesteepest CO ladders observed so far. Sub-mm data reveal presence of (one ormore) bright companion galaxies around 80% of WISSH QSOs, at projecteddistances of 6-130 kpc. We observe a variety of sizes for the molecular gasreservoirs (1.7-10 kpc), associated with rotating disks with disturbedkinematics. WISSH QSOs typically show lower CO luminosity and higher starformation efficiency than FIR matched, z~0-3 main-sequence galaxies, implyingthat, given the observed SFR ~170-1100 $M_\odot$/yr, molecular gas is convertedinto stars on <50 Myr. Most targets show extreme dynamical to black-hole massratios $M_{\rm dyn}/M_{\rm BH}\sim3-10$, two orders of magnitude smaller thanlocal relations. The molecular gas fraction in WISSH hosts is lower by a factorof ~10-100 than in star forming galaxies with similar $M_*$. WISSH QSOs undergoan intense growth phase of both the central SMBH and host-galaxy. They pinpointhigh-density sites where giant galaxies assemble and mergers play a major rolein the build-up of the final host-galaxy mass. The observed low molecular gasfraction and short depletion timescale are likely due to AGN feedback, astraced by fast AGN-driven ionised outflows in all our targets.

The WISSH QSOs project IX. Cold gas content and environment of luminous QSOs at z~2.4-4.7