The assembly of the first super massive black holes (SMBHs) at z 6 is still a subject of intense debate. If black holes (BHs) grow at their Eddington rate, they must start from 10 4 M ⊙ seeds formed by the direct collapse of gas. Here we explore the alternative scenario where ∼ 100 M ⊙ BH remnants of the first stars grow at super-Eddington rate via radiatively inefficient slim accretion disks. We use an improved version of the cosmological, data-constrained semi-analytic model GAMETE/QSOdust, where we follow the evolution of nuclear BHs and gas cooling, disk and bulge formation of their host galaxies. Adopting SDSS J1148+5251 (J1148) at z = 6.4 as a prototype of luminous z 6 quasars, we find that ∼ 80% of its SMBH mass is grown by super-Eddington accretion, which can be sustained down to z ∼ 10 in dense, gas-rich environments. The average BH mass at z ∼ 20 is M BH 10 4 M ⊙ , comparable to that of direct collapse BHs. At z = 6.4 the AGN-driven mass outflow rate is consistent with the observations and the BH-to-bulge mass ratio is compatible with the local scaling relation. However, the stellar mass in the central 2.5 kpc is closer to the value inferred from CO observations. Finally, ∼ 20% of J1148 progenitors at z = 7.1 have BH luminosities and masses comparable to ULAS J1120+0641, suggesting that this quasar may be one of the progenitors of J1148.

Observations of the most luminous quasars at redshift z > 6 reveal the existence of numerous supermasssive black holes (> 10 9 M⊙) already in place about twelve billion years ago. In addition, the interstellar medium of the galaxies hosting these black holes are observed to be chemically mature systems, with metallicities (Z > Z⊙) and dust masses (> 10 8 M⊙) similar to that of more evolved, local galaxies. The connection between the rapid growth of the first supermassive black holes and the fast chemical evolution of the host galaxy is one of the most puzzling issues for theoretical models. Here we review state-of-the-art theoretical models that focus on this problem with particular emphasis on the conditions that lead to the formation of quasar seeds and their subsequent evolution at z ≥ 6.