Multiplier onions exist in two horticultural forms: potato onions and shallots. Walking onions are a different group.
Potato Onions, Multiplier Onions, Shallots: (Allium cepa var. aggregatum) These perennial onions are planted whole in the fall or late winter and subdivide the following spring.
Egyptian Walking Onions: (Allium cepa var. proliferum) These topsetting onions are grown primarily for their hardy greens.
Perennial Leeks: (Allium ampeloprasum) Easily propagated by divisions.
According to the National Gardening Bureau, multiplier onions can produce a larger yield per area than any other vegetable except staked tomatoes.
Multiplier onions produce a cluster of bulbs at ground level from a single planted bulb. The larger bulbs are saved for eating, and the medium and small bulbs are stored and replanted.
There are several advantages of growing multiplier onions: (1) They are not as readily bothered by the onion fly as are seed onions. (2) Once you have enough potato onions or shallots you need not buy seeds or sets again. (3) Some types of multiplier onions are in demand as gourmet items in restaurants. (4) Potato onions and many shallots store well, and can withstand subfreezing temperatures in every area of the continental U.S. when properly planted.
Where to buy potato onions: Southern Exposure seeds have had them for sale for a long time and are probably partly responsible for keeping potato onions alive: http://www.southernexposure.com
Perennial Onion Growing Guide : Southern Exposure Seed Exchange, Saving the Past for the Future http://buff.ly/2k0Cfux
Jung Seed http://buff.ly/2k0JmDm
Yellow Potato Onion 8 oz. : Southern Exposure Seed Exchange, Saving the Past for the Future http://buff.ly/2kkiOZC
All Garlic & Shallots - Yellow Multiplier Onion http://buff.ly/2kkiUQY
Garlic and Perennial Onion Growing Guide : Southern Exposure Seed Exchange, Saving the Past for the Future http://buff.ly/2liv29C