Catheter assembly (100) having at least one lumen (150 or 160) and joined to hub (106). While the lumen inner diameter(s) remain constant from distal end (144) of the catheter (140) to proximal end (142), the outer catheter diameter increases proximate the hub (106) providing increased resistance to kinking during connection and disconnection from medical apparatus. The increased proximal catheter diameter preferably is sufficiently large to plug the proximal end of an introducer sheath through which the catheter is inserted during patient placement, to plug the proximal sheath end and minimize blood aspiration therethrough, and later serves to fill the vascular insertion upon complete catheter insertion after removal of the introducer sheath again to minimize blood aspiration through the vascular incision. The catheter may have two lumens (150,160) or more, joined to respective extension tubes in hub (106). The two lumens may each have a respective inner diameter of between about 0.020 in and 0.025 in. The catheter body may have a lengthy distal portion vascularly implanted having an appropriate outer diameter for the vessel, and also a lengthy proximal portion with a larger diameter for resistance to kinking at a sharp bend between the vascularly implanted portion and the subcutaneously tunneled lengthy proximal portion.