Natal kicks, v_kick, as generated by NBODY7, as a function of m_CO (left panel) and m_rem (right panel), for the different natal-kick recipes considered in this work. The F12-rapid+B16-PPSN/PSN remnant-mass model (Sect. 2.2) and Z = 0.0001 is assumed. Because of the logarithmic vertical axis, direct-collapse BHs with f_fb = 1 and v_kick = 0 are not shown in these panels; the sharp drop in v_kick with increasing m_CO or m_rem is the approach towards direct collapse. The typical v_esc for the M_cl(0) ≈ 5.0 × 10⁴ M_⊙, r_h(0) ≈ 2 pc clusters considered in this study (blue, solid line) and the Hobbs et al. (2005)σ_NS ≈ 265 km s⁻¹, whose value in all the kick models are scaled (see Sects. 3.1 and 3.2; black, solid line), are indicated.