Do z>6 quasars reside in protoclusters?

We discuss the properties of a sample of z>6 bright (bolometric luminosity L$_{\rm bolo}$>10$^{46.25}$ erg/s) Quasars drawn from a realisation of the GAlaxy Evolution and Assembly (GAEA) model coupled with the Planck Millennium Simulation. We focus on the properties and environment of host galaxies on a physical scale of 10 cMpc, and their evolution down to z=0, with the aim of assessing how well the bright high redshift QSOs population traces the progenitors of the most massive haloes in the local Universe. GAEA predicts that z>6 bright QSOs live in a variety of environments, and that secular processes like disc instability are responsible for triggering roughly the same number of QSOs as galaxy mergers. We consider mock fields built around these high-z QSOs, and we show that roughly half of them include other active galaxies (with L$_{\rm bolo}$>10$^{44}$ erg/s). The predicted large field-to-field variance in the number of companions is qualitatively consistent with recent results from JWST observations. Descendants of host galaxies at z=0 cover a wide range of physical properties and environments with only a small fraction of them belonging to massive galaxy clusters (M$_{\rm DM}$>10$^{14.5}$ M$_\odot$). Viceversa, GAEA predicts that only a small fraction of Bright Central Galaxies have a bright z>6 QSOs among their progenitors. Our results suggest that luminous high-z QSO loosely trace the progenitors of low-z galaxy clusters, but that additional information about their environment (like the number of active galaxy companions) are required to identify the most promising proto-cluster candidates.