An apparatus for positioning a graft and catheter operable for subcutaneous access to the vascular system of a patient. A surgically created, hybrid arteriovenous shunt is provided which comprises a flexible graft and a venous outflow catheter connected to the graft via surgical anastomosis over a cuff. The graft is connected to an arterial source and then to a single lumen venous outflow catheter which deposits dialyzed blood directly into the heart at the right atrium. Methods of surgical placement and performing hemodialysis using embodiments of the apparatus are provided.