Left panel: Population synthesis of 5000 planets for an irradiated disc, with linear scaling of the gas accretion rate with stellar masse (Eq. 1, β = 1), randomly sampled Z, and disc lifetimes from Gaussian distributions (Appendix B.1), and M_★ from the Chabrier (2005) IMF restricted to the range 0.01 − 5 M_⊙. The colour-coding shows the disc lifetime. Right panel: Same as the left panel but for a moderately accretion-heated disc. The bottom left box shows the occurrence fraction of the different types of planets in both cases. We chose to use as a fiducial model the moderately accretion-heated disc (right panel) as the occurrence rate of super-Earths is broadly consistent with observations (Zhu et al. 2018).