The main source feeding the abyssal circulation of the North Pacific is the deep, northward flow of 5–6 Sverdrups (Sv; 1 Sv ≡ 10$^6$ m$^3$ s$^{−1}$) through the Samoan Passage. A recent field campaign has shown that this flow is hydraulically controlled and that it experiences hydraulic jumps accompanied by strong mixing and dissipation concentrated near several deep sills. By our estimates, the diapycnal density flux associated with this mixing is considerably larger than the diapycnal flux across a typical isopycnal surface extending over the abyssal North Pacific. According to historical hydrographic observations, a second source of abyssal water for the North Pacific is 2.3–2.8 Sv of the dense flow that is diverted around the Manihiki Plateau to the east, bypassing the Samoan Passage. This bypass flow is not confined to a channel and is therefore less likely to experience the strong mixing that is associated with hydraulic transitions. The partitioning of flux between the two branches of the deep flow could therefore be relevant to the distribution of Pacific abyssal mixing. To gain insight into the factors that control the partitioning between these two branches, we develop an abyssal and equator-proximal extension of the “island rule.” Novel features include provisions for the presence of hydraulic jumps as well as identification of an appropriate integration circuit for an abyssal layer to the east of the island. Evaluation of the corresponding circulation integral leads to a prediction of 0.4–2.4 Sv of bypass flow. The circulation integral clearly identifies dissipation and frictional drag effects within the Samoan Passage as crucial elements in partitioning the flow.