Can you cook cut potatoes in a nonstick frying pan without oil

Yes, you can.

The problem is that the potatoes start absorbing water, and you end up with a really runny mash that's difficult to flavor (as most people flavor their mash by the addition of flavorful liquids).

update : There's a few things that you can do to hold them. The first is to drain the water, and leave the potato bits (unmashed) in the pot. If you leave them uncovered, they'll cool off, but it'll also let moisture evaporate, which can help to fix some of the problems I mentioned earlier.

You don't want to let them cool off too far, or they'll not mash up smoothly; if you're going to need to hold them for more than 5-10 minutes, put a lid on them. Once it comes time to mash, refresh them with whatever liquid you're going to add to the mash, warmed.

If you're going to need to hold them a really long time, you have two options ... one is to mash them but intentionally reduce the liquid, and then refresh them with more hot liquid a few minutes before serving. The other is to transfer them to a baking dish after mashing, and put it in a low oven. (if you rough up the surface, and put it under the broiler right before serving, you can get a crust on it for a bit of variety).

The coating you are talking about is potato starch that is browning on the bottom of the pan, similar to what happens to roux when it is prepared. If you deglaze the pan using alcohol, it will come right off without any effort (water works too, though more is needed).

As for how to get the potatoes not to stick, it's important that the pan and the oil are quite hot when the potatoes are added to the pan. As described at Newton Ask a Scientist, the hot oil encourages a steam barrier to appear between the potatoes and the pan, temporarily protecting the potatoes from sticking and encouraging the formation of a crust that will permanently keep them from sticking. Depending on the amount of potato being cooked, the amount of oil added to the pan will have to be adjusted for thermal mass, since the addition of uncooked potatoes will cause the oil to cool down very quickly.