Black hole spin magnitudes as a function of the orbital period for our Z = 0.014 (circles) and Z = 0.0004 (triangles) MESA models. The color coding corresponds to the black hole remnants with masses: M_BH <  15 M_⊙ (black/blue), 15 M_⊙ <  M_BH <  30 M_⊙ (cyan/red), M_BH >  30 M_⊙ (green/magenta). Binary systems with short orbital periods: 0.1−1.3 d and WR stars will produce BHs with broad range of spin magnitudes: 0.15−1. Systems with orbital periods below 0.1 d form black holes from tidally locked WR stars, and the BH spins are maximal. Binaries with an orbital period above 1.3 d produce BHs with spins below 0.2 and typically are not tidally locked at all. A set of the most massive, lowest-metallicity stars have such dense cores that tidal spin-up does not dramatically increase their angular momentum and these stars require orbital periods of less than 0.1 d to have spin values above 0.1 (lower set of green triangles). However, we ignore this fact, and let these cores to be spun-up to estimate the maximal effect of tidal interactions in our models (higher set of green triangles). The black curve shows our fit to the BH spin magnitude as a function of orbital period.