The assembly comprises two or more catheter tubes fused together to form a fused catheter bundle. Each tube has at least one lumen extending longitudinally through the catheter from its distal end to its proximal end and wherein at least one of said tubes comprises a pressure resistant lumen. The tubes are fused together by use of heat & pressure generated by heat shrinkable tube slides positioned over a segment of the catheter tubes while mandrels are positioned within each tube lumen. After cooling, the heat shrinkable tube may be removed and the mandrels removed such that and the fused catheter bundle is formed. One or more of the tubes may be of a different hardness, material and/or color. A distal end of the fused catheter bundle can be split free floating, stepped or tapered tipped. A non fused portion may form catheter extension legs.