Ok, so you're going to have to plant those puppies in the ground or a large pot somewhere. They won't grow plants like that. See where you're getting leaves on the right side of the potato? That is a new plant starting. Every "eye" on that potato might make a new plant. The eyes are the little things that look like belly buttons.
So you should cut the potato up into chunks, each with an eye, and let the cut edges dry, then plant each piece with an eye so that the eye can "see" the sun. i.e. bury the potato piece all except the eye.
Once the plant is growing, you should mound up the soil around the stems as it gets taller. That way the plant will produce more potatoes on the buried stems.
The way you have it growing now, it won't make a plant that will produce potatoes. In fact, I'm surprised the bottom part in the water hasn't rotted yet. Avocado will sprout like that, but not potatoes.