I planted some potatoes in the fall the way Paul Gautschi does in his Back to Eden garden. As he is harvesting he puts the largest most perfect potatoes back in. He does not cut the potatoes up either, as that is not how it would happen in nature.
This is the result of the experiment so far. I did this short row as a test. Doesn't it look great. The potato plants are about six inches tall. So far so good. I am going to plant the very large potato patch the conventional way...ie plant in the spring, but I will switch the whole system over at harvest time.