A device for enabling sequential dilation of a percutaneous tissue opening to seccessively larger opening sizes. The device includes a first-elongated dilator element having a forward end, an intermediate dilator body and a tail section extending from shoulder structure at the junction of the intermediate body and tail section. At least one additional elongated tubular dilator is adapted for telescopic mounting over the first dilator element and includes a forward end, intermediate body, rearward end and blocking member. This dilator is tubular in construction and sized to fit snugly around the first dilator element in telescoping manner. The blocking member positioned at a rearward end of the dilator allows it to be seated in a forward-most position, in contact with the shoulder structure of the first dilator element. Additional dilators of successively larger diameters can be added to increase the extent of tissue dilation. Removal of the dilator device is accomplished by grasping the tail section and withdrawing the system from within a sheath or cannula emplaced to link a patient to an extracorporeal circulatory system.