The blood from the upper limb is returned to the heart by two sets of veins, superficial and deep. Both sets have valves, and both drain ultimately into the axillary vein. Superficial Veins (fig. 7-1).The superficial veins are highly variable, lie mostly in the subcutaneous tissue, and return almost all of the blood.Digital veins drain into a dorsal venous network in the hand, which leads to two prominent veins, the cephalic and the basilic.oth sets have valves, and both drain ultimately into the axillary vein. Superficial Veins (fig. 7-1). The superficial veins are highly variable, lie mostly in the subcutaneous tissue, and return almost all of the blood.