Black hole growth in rotating FFB clusters with a broad IMF. Same as Fig. 2, right panel, based on Eq. (3) (Rizzuto et al. 2021, Eq. (4)), but with t_cc reduced by a factor of 10 due to rotation (gravo-gyro instability; Hachisu 1979, 1982; Hong et al. 2013; Kamlah et al. 2022) and flattening. The FFB clouds that form by disk instability at the characteristic Toomre mass of ∼10⁷ M_⊙ (Dekel et al. 2023a), lie above the curve (magenta) that marks core-collapse in 3 Myr. However, if sub-Toomre clouds form by fragmentation with the same Σ, they should lie along the red line, such that core collapse will occur in 3 Myr for M_c ≤ 10⁶ M_⊙. The corresponding black-hole mass at the end of the FFB phase, Eq. (5), is M_bh ≤ 10⁴ M_⊙ (top axis).