We plot k = Ω_F/Ω_H and its dependence on spin, which is crucial for converting jet power into angular momentum in our semi-analytic model. The red-dashed line shows the fit that we used to construct our semi-analytic model for a > 0. We did not find a strong dependence on spin for a < 0 and so used a constant value, k = 0.23, in our semi-analytic model for a < 0.