Left panel: fraction of ﹩{\dot{M}}_{{\rm{Hill}},\,{\rm{net}}}﹩ (integrating down to μ = μ_CPD by choice; see Equation (18)) that falls directly onto the planet (﹩{\dot{M}}_{{\rm{p}},\,{\rm{direct}}}﹩). Black (gray) dots are for the assumption of f_cent = 0.03 (1/3). Right panel: comparison of the mass influx falling directly onto the planet when calculated in our setup (Gaussian density profile at the outer edge and CPD-caused truncation of the equatorial inflow; Equations (15) or (17)) relative to the result from a constant vertical density at the Hill radius integrated down to the equator (“Isotropic” case in A. G. Taylor & F. C. Adams 2024).