Left: probability distribution function (PDF) of the orbital periods P_WR–BH at the end of the WR–BH configuration for progenitors of BBHs. The dashed line at P_WR–BH = 1 day highlights the systems that are tight enough to induce efficient tidal spin-up (P_WR–BH ≤ 1 day) according to the model by Bavera et al. (2021b). Center: probability distribution function of the dimensionless spin magnitude χ_{BH, 2} of second-born BHs in WR–BHs evolving into BBHs. Spins are calculated with the model of Bavera et al. (2021b) that assumes tidal spin-up in close binaries and efficient angular momentum transport. All the 96 simulated sets (Table 1) exhibit a bimodal distribution. Right: probability distribution function of the effective spin parameter χ_eff obtained in all 96 sets, color-coded according to the assumed metallicity Z.