In eukaryotic cells, nanotubes represent a substantial fraction of transport intermediates between organelles. They are extracted from membranes by molecular motors walking along microtubules. We previously showed that kinesins fixed on giant unilamellar vesicles in contact with microtubules are sufficient to form nanotubes in vitro. Motors were attached to the membrane through beads, thus facilitating cooperative effects. Koster et al. proposed that motors could dynamically cluster at the tip of tubes when they are individually attached to the membrane. We demonstrate, in a recently designed experimental system, the existence of an accumulation of motors allowing tube extraction. We determine the motor density along a tube by using fluorescence intensity measurements. We also perform a theoretical analysis describing the dynamics of motors and tube growth. The only adjustable parameter is the motor binding rate onto microtubules, which we measure to be 4.7 +/- 2.4 s(-1). In addition, we quantitatively determine, for a given membrane tension, the existence of a threshold in motor density on the vesicle above which nanotubes can be formed. We find that the number of motors pulling a tube can range from four at threshold to a few tens away from it. The threshold in motor density (or in membrane tension at constant motor density) could be important for the understanding of membrane traffic regulation in cells.