  Sources at the brightest end of QSO luminosity function during the peak epoch
of star formation and black hole accretion (z~2-4, i.e. Cosmic noon) are
privileged sites to study the feeding & feedback cycle of massive galaxies. We
perform the first systematic study of cold gas properties in the most luminous
QSOs, by characterising their host-galaxies and environment. We analyse ALMA,
NOEMA and JVLA observations of FIR continuum, CO and [CII] emission lines in
eight QSOs ($L_{\rm Bol}>3\times10^{47}$ erg/s) from the WISSH sample at
z~2.4-4.7. 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-mm 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), associated with rotating disks with disturbed
kinematics. WISSH QSOs typically show lower CO luminosity and higher star
formation efficiency than FIR matched, z~0-3 main-sequence galaxies, implying
that, given the observed SFR ~170-1100 $M_\odot$/yr, molecular gas is converted
into stars on <50 Myr. Most targets show extreme dynamical to black-hole mass
ratios $M_{\rm dyn}/M_{\rm BH}\sim3-10$, two orders of magnitude smaller than
local relations. The molecular gas fraction in WISSH hosts is lower by a factor
of ~10-100 than in star forming galaxies with similar $M_*$. WISSH QSOs undergo
an intense growth phase of both the central SMBH and host-galaxy. They pinpoint
high-density sites where giant galaxies assemble and mergers play a major role
in the build-up of the final host-galaxy mass. The observed low molecular gas
fraction and short depletion timescale are likely due to AGN feedback, as
traced by fast AGN-driven ionised outflows in all our targets.
