My Mom had a real thing about covering veggies with water to boil them. It drove her around the bend when she would see someone doing it. Her view was that unless you drank the water or used it in some other way, you were throwing always all the nutrients; I kind of think so myself.
I put in enough water to cover the potatoes a third of the way; sprinkle with salt, cover, bring to a boil, turn the heat down to medium low and cook approximately 15 – 20 minutes until you can easily pierce with a skewer or thin blade knife but not overcooked. I believe Mom was right, the veggies taste better!
The only time I don’t follow this method is when I boil potatoes for gnocchi. Chef, Lydia Bastianich knows a thing or two about gnocchi so I take her word for it!