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The first four gravitational wave events detected by LIGO were allinterpreted as merging black hole binaries (BHBs), opening a new perspective onthe study of such systems. Here we use our new population-synthesis code MOBSE,an upgraded version of BSE (Hurley et al. 2002), to investigate the demographyof merging BHBs. MOBSE includes metallicity-dependent prescriptions for massloss of massive hot stars. It also accounts for the impact of theelectron-scattering Eddington factor on mass loss. We perform >10^8 simulationsof isolated massive binaries, with 12 different metallicities, to study theimpact of mass loss, core-collapse supernovae and common envelope on mergingBHBs. Accounting for the dependence of stellar winds on the Eddington factorleads to the formation of black holes (BHs) with mass up to 65 Msun atmetallicity Z~0.0002. However, most BHs in merging BHBs have masses <40 Msun.We find merging BHBs with mass ratios in the 0.1 - 1.0 range, even if massratios >0.6 are more likely. We predict that systems like GW150914, GW170814and GW170104 can form only from progenitors with metallicity Z<=0.006, Z<=0.008and Z<=0.012, respectively. Most merging BHBs have gone through a commonenvelope phase, but up to ~17 per cent merging BHBs at low metallicity did notundergo any common envelope phase. We find a much higher number of mergers frommetal-poor progenitors than from metal-rich ones: the number of BHB mergers perunit mass is ~10^-4 Msun^-1 at low metallicity (Z = 0.0002 - 0.002) and dropsto ~10^-7 Msun^-1 at high metallicity (Z ~ 0.02).

Merging black hole binaries: the effects of progenitor's metallicity, mass-loss rate and Eddington factor