Remnant masses (m_RN), as function of ZAMS mass (m_ZAMS). The blue curve shows the remnant function for case A and case B mass transfer, based on the simulations by Marchant et al. (2019) and Schneider et al. (2021). The Marchant et al. (2019) results are shown as well (black dots). The triangle shows the transition point between the part of our function which is based on Schneider et al. (2021) and the part which is based on Marchant et al. (2019). The red curve shows the corresponding remnant function for case C mass transfer, where the part after the transition point is the PPISN fit translated to lower masses by 42 M_⊙. The dashed lines show m_RN/m_ZAMS = 1, 0.65 and 0.35, since the latter two are used as approximation in estimating the amount of mass transfer in our estimation. The shaded area shows the values of the remnant mass gap. Furthermore, we note that this remnant function is limited to BHs, as for our purposes, we are not interested in the neutron star (NS) masses. The remnant functions are explicitly given in Appendix C.