The present invention is TAH system for auto-regulating blood flow and maintaining the asymmetric pressure balance in the mammalian cardiovascular system by decreasing the resistance in blood flow and minimizing the pressure gradients to exploit the in-flow pressure sensitivities of continuous flow pumps. The system further includes laminar flow generating manifolds connected to the atrium at one end and attached to pumps linked to the great vessels at the other, such that the in-let flow sensitivities of the pumps are maximized to auto-regulate blood flow, providing adequate pulmonary and systemic arterial flow to support normal metabolism and end-organ function and maintain the appropriate asymmetric physiologic pressure balance between the systemic and pulmonary systems of the mammalian cardiovascular system.