Inflow functions (that is, mass loading at the Hill sphere) as in A. G. Taylor & F. C. Adams (2024; colored lines) and with an example of our adaptation for massive accreting planets (“Gaussian”; R_Hill/H_{P, PPD} = 2.4; see Equation (8)), either truncating the inflow approximately at the thickness of the CPD (black line) or allowing it down to the midplane (gray dashed). Only the gas between the pole (θ₀ = 0) and θ_0→p = 8﹩\mathop{.}\limits^{\unicode{x000b0}}﹩3 (Equation (16), for the reference values in Equation (8) and R_p = 2R_J) hits the planet surface directly, with the rest landing on the CPD.