A catheter tunneling adapter including a generally elongated body having a proximal end, a distal end and a through passageway. The proximal end of the adapter is connectable both to a proximal hub of a stylet and subsequently to the distal end of a tunneler. The distal end of the adapter comprises a connector for connecting a plurality of proximal catheter tubes thereto, wherein the proximal end of one tube is affixed within the passageway at the adapter's distal end and the proximal end of the second tube is plugged by a plug extending distally from a free end of an elongate flexible arm that also extends distally of the adapter's distal end, such that the plug is offset laterally therefrom. The flexible arm and the affixed second tube end are deflectable toward the first tube to reduce the profile of the assembly during tunneling.