the $j-gas$ particle inside the cell. The normalization constant is defined by $A = 1/\sum_j r^n_{ij}$ . Different values of the exponent (n = 2, 4) were tested. Supernovae do not only contribute to the energy budget of the interstellar medium but also inject heavy metals, leading to a progressive chemical enrichment of galaxies as well as of their nearby environment. Such a progressive enrichment was treated by an adequate algorithm able to simulate the turbulent diffusion of metals trough the medium.

In the code, BHs are represented by collisionless particles that can grow in mass, according to specific rules that mimic accretion or merging with other BHs. Possible recoils due to a merging event and to the consequent emission of gravitational waves were neglected. BHs are assumed to merge if they come within a distance comparable to or less than the mean inter-particle separation. Seeds are supposed to have been formed from the first (very massive) stars and are supposed to have a mass of about 100 $M_\odot$. An auxiliary algorithm finds potential minima where seeds are inserted in the redshift interval $15-20$. A fraction of the energy released during the accretion process is re-injected into the medium along 