Basil - where does the new growth come from?

I have grown basil like other herbs for a long time, and without thinking about it I simply pick off the leaves as I go, not employing any special techniques. The next day the leaves have been replaced. Sometimes there are tiny leaves growing in the leaf axil of the existing ones, or else other dormant buds elsewhere along the stem, but the exact ones pulled off also seem to be replaced.
I have just pulled a small leaf from a basil plant now. This leaves a tiny fleshy "stub" (the redundant petiole or leaf stem) but I cannot see any more along the stem, though it has certainly had leaves taken from it in the past. Can the new leaves simply grow back on the same leaf stem? Or does this stub die down and disintegrate?