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We leveraged low to high frequency ALMA observations to investigate the coldgas and dust in 10 QSOs at $z\gtrsim 6$. Our analysis of the CO(6-5) andCO(7-6) emission lines in the selected QSOs provided insights into theirmolecular gas masses, averaging around $10^{10}\ \rm M_\odot$, consistent withtypical values for high-redshift QSOs. Proprietary and archival ALMAobservations in bands 8 and 9 enabled, for the first time, precise constraintson the dust properties and SFR of 4 QSOs in our sample. Examination of theredshift distribution of dust temperatures revealed a general trend ofincreasing $T_{\rm dust}$ with redshift, which is in agreement with theoreticalexpectations. On the contrary, investigation of the dust emissivity indexindicated a generally constant value with redshift, suggesting shared dustproperties among sources. We computed a mean cold dust SED considering all 10QSOs that offers a comprehensive view of high-$z$ QSO's dust properties. TheQSOs marked by more intense supermassive black hole growth (HYPERION QSOs)showed -- on average -- smaller dust masses and higher gas-to-dust ratios,while having $\rm H_2$ gas reservoirs consistent with other QSOs at the sameredshift. Beyond supporting the paradigm that high-$z$ QSOs reside in highlystar-forming galaxies, our findings portrayed an interesting evolutionary pathat $z>6$. Our study suggested that QSOs at $z\gtrsim 6$ are undergoing rapidgalaxy growth, potentially regulated by strong outflows. In the $M_{\rmBH}-M_{\rm dyn}$ plane, our high-$z$ QSOs lie above the relation measuredlocally. Their inferred evolutionary path portends a convergence towards themassive end of the local relation, supporting their candidacy as progenitors oflocal massive galaxies. The observed pathway involves intense BH growthfollowed by substantial galaxy growth, in contrast with a symbiotic growthscenario.

HYPERION. The SMBH-galaxy co-evolution at $z>6$ and the build-up of massive galaxies