Top panels: SFR-M_⋆ plane at z = 2.8 for the Gonzalez-Perez14 model. Both panels show as coloured contours the number densities of quasars with luminosities in the Bj band >10^44.5 erg s^-1 (left panel) and of all galaxies in the model (right panel). Number densities correspond to the number per volume, per unit logM_⋆ and logSFR (as indicated by the colour bar). The dashed black line indicates the main sequence of star-forming galaxies at a redshift 2 <z< 2.5 (Tacconi et al. 2013). In addition, we show in the right panel as black contours the number density of all galaxies with SFR> 100 M_⊙ yr^-1 that are at <250 kpc physical distance of a bright quasar (L_Bj> 10^44.5 erg s^-1). Solid and dashed contours show the number densities of 10^-5.9 and 10^-5 Mpc^-3h³ dex^-2. These number densities are equivalent to ≈2 and ≈16 galaxies in the simulated volume, respectively. This figure shows that the subset of highly star-forming galaxies living nearby bright quasars are about a tenth of all the highly star-forming galaxies. In the right panel we show two examples of quasar–companion galaxy pairs indicated by empty (quasar) and filled (companion) squares. These pairs are very similar to SMM J04135+10277, they have an integrated SFR> 300 M_⊙ yr^-1 and the distance between the components is <50 kpc. Bottom panels: as in the top panels but for a variant of the Gonzalez-Perez14.GRP model.