Evolution of the MT rate and overflow for a system with a 30 M_⊙ donor star, a 7.5 M_⊙ BH, and an initial orbital period of 31.6 days. Top: ratio of the computed MT rate under different assumptions, compared to the result from our full MT prescription. Middle: ratio of the stellar radius to the Roche lobe radius and to the volume equivalent radius of the L₂ and L₃ equipotentials (for the L₂ equipotential, we only include the results of our default model for ease of visualization). Bottom: MT rate.