Place the ham hock('s) and onion into a 4 quart Dutch oven and fill half way full with water.
Season water with salt, pepper and garlic powder and bring to a boil, then cover and simmer over low heat until meat falls off the bones, about 2 hours. Remove the bones and skin; return the meat to the pot.
Discard bones and skin.
Add the green beans to the Dutch oven and simmer for 20 minutes, then add the potatoes. Simmer for 10 to 15 minutes more, or until they can be easily pierced with a fork.