(a) Dark matter mass (M_DM) and stellar mass (M_*) distribution of halos that host GCs capable of forming MBBHs. (b) Two-dimensional density distribution of GCs in the mass-metallicity plane. The contours represent the density estimation of the cluster population, highlighting the regions where initial central stellar number density and total mass facilitate MBBH formation, with color gradients distinguishing between high initial central number density (red-yellow tones, ρ_c > 5 × 10⁷ pc⁻³) and lower initial central density (blue-green tones, ρ_c < 5 × 10⁷ pc⁻³).