Methods and devices are disclosed for connecting implantable body fluid conduits, such as catheters and grafts for AV shunts. A connector with thin connector walls at the lumen openings provides a connecting lumen that is close to flush with the lumens of the attached conduits. A tapered, smooth walled connector lumen allows connection of conduits with different internal diameters while preserving laminar flow in the transition between different conduit diameters. Rounding of the connector edges at the lumen openings further reduce disturbances in flow.
