Fraction of galaxies in which BH formation is driven by the condition t = t_coll as a function of the power-law exponents α and β . The x-axis represents the exponent in the mass-radius relation $R_{\mathrm{gal}}\propto M_{\mathrm{gal}}^{\beta }$, and the y-axis represents the exponent in the mass-time relation M_gal ∝ t^α. The color bar shows f_coll and indicates the percentage of galaxies in which BH formation specifically satisfies t = t_coll.