Last year, I put aside a certain amount of space I wanted to fill with potatoes. I cut up my potatoes and found I still had more space to use up. I was in a hurry and just filled the rest of the space up with whole potatoes. I didn't seem to notice much of a difference. Could of been the kind of potato, I think the extra was Bintje. I love that potato. I usually plant four and it is my favorite.
I believe, from my experience, that a onion left over from the year before that starts to sprout will bolt and give you lots of seeds for the next year but not much of a bulb.
You could leave the turnips and collect seeds for next year form them.