Context. Sources at the brightest end of the QSO luminosity function (LBol > 1047 erg s􀀀1) during the peak epoch in the history of star formation and black hole accretion (z 2 􀀀 4, often referred to as "Cosmic noon") are privileged sites to study the cycle of feeding & feedback processes in massive galaxies. Aims. We aim to perform the first systematic study of cold gas properties in the most luminous QSOs, by characterising their host-galaxies and environment. These targets exhibit indeed widespread evidence of outflows at nuclear and galactic scales. Methods. We analyse ALMA, NOEMA and JVLA observations of the far-infrared continuum, CO and [CII] emission lines in eight QSOs (bolometric luminosity LBol & 3 1047 erg s􀀀1) from the WISSH sample at z 2:4 􀀀 4:7. Results. We report a 100% emission line detection rate and a 80% detection rate in continuum emission, and we find CO emission to be consistent with the steepest CO ladders observed so far. Sub-millimetre data reveal presence of (one or more) bright companion galaxies around 80% of WISSH QSOs, at projected distances of 6 􀀀 130 kpc. We observe a variety of sizes for the molecular gas reservoirs ( 1:7 􀀀 10 kpc), mostly associated with rotating disks with disturbed kinematics. WISSH QSOs typically show lower CO luminosity and higher star formation e ciency than infrared matched, z 0􀀀3 main-sequence galaxies, implying that, given the observed SFR 170􀀀1100 M yr􀀀1, molecular gas is converted into stars in . 50 Myr. Most targets show extreme dynamical to black-hole mass ratios Mdyn=MBH 3 􀀀 10, two orders of magnitude smaller than local relations. The molecular gas fraction in the host-galaxies of WISSH is lower by a factor of 10 􀀀 100 than in star forming galaxies with similar M . Conclusions. Our analysis reveals that hyper-luminous QSOs at Cosmic noon undergo an intense growth phase of both the central SMBH and of the host-galaxy. These systems pinpoint the high-density sites where giant galaxies assemble, where we show that mergers play a major role in the build-up of the final host-galaxy mass. We suggest that the observed low molecular gas fraction and short depletion timescale are due to AGN feedback, whose presence is indicated by fast AGN-driven ionised outflows in all our targets.