Function S(a₀) given different assumptions on the dynamics and treatment of two-body relaxation. For the dynamics, we distinguish between Newtonian (N) or PN evolution of the system, and between employing the equations detailed in Peters (1964) or the 2.5PN term to treat loss of energy and angular momentum due to GW emission. Instead, two-body relaxation can be accounted for using the orbit-averaged approximation (indicated with OA), or locally. In all cases M_• = 3 × 10⁵ M_⊙ and the MBH is surrounded by a distribution of m_⋆ = 1 M_⊙ stars only.