How little potato root is needed to produce foliage?

[Stephen]

As it says really.
After I cleared the onion bed (which had several volunteers) I cleared the ground yet I am still getting some sprouts. When I lift these there appear to be no tubers underneath.
Also relevant as I have gone over this year's row of earlies twice I was wondering if I should dig over a third time?

[glallotments]

It is amazing - after an incredibly dry growing season - we have had hardly any significant rain since April, our potato tops had made very little growth. We dug them up fearing we would have nothing to harvest but have had a good a crop in weight as last year. The only real difference is fewer individual potatoes but larger tubers.