Place whole pieces of corned beef in a large 5 gallon stock pot, or one each into 3 pots.
Cover with water. Bring to a boil. Cover and simmer about, 3- 5 hours or until tender, depending on the size of the meat. (As the meat is cooking, skim off the scum that accumulates on the surface.)
Remove tender corned beef from liquid.
Remove any excess fat from top of liquid. Pour liquid into a roasting pan or other pan with a larger top surface which can be used for cooking vegetables.
Bring cooking liquid to a boil. Add carrots, rutabagas, and onions.
Cook 10 min. Add potatoes to vegetables.
Return to a boil and continue to cook another 10 min.
Place cabbage wedges on top of vegetables in broth and continue to cook another 15 minutes. Drain when tender, don't let potatoes sit in water.
Serve vegetables hot with thin slices of corned beef.