Time series of the mass accretion rates |$\dot{M}_1$| (top), |$\dot{M}_2$| (middle), and |$\dot{M}_2/\dot{M}_1$| (bottom) for a binary mass ratio of |$q = 0.01$| and a gas orbital Mach number of |$\mathcal {M} = 10$|⁠, with varying sink rates and a sink size of |$r_{\rm sink} = 0.05 a_0$|⁠. Each line starts as a solid curve and transitions to a dashed curve at the time when the secondary BH sink radius becomes comparable to the size of the Hill radius, beyond which the gas flow in the secondary disc is not well resolved for the dashed curves.