Onions are smart, and show their wits when allowed to perennialize. They will propagate themselves by seed and by division, putting more energy into seed when they are stressed, and more into vegetative growth (division) when conditions are good.

Hmmm. Can I extrapolate from this that if I were to plant the onion, that it would continue to separate, thereby making a clump or will the sneaky little buggers just set seed? By the way, I am in an elevation that is not conducive to bulb growth except for the small, --we call them "Filipino" onions--that have tiny purple, ovoid bases; very similar to the l-toi. Sigh. I long to have an onion patch of onions that are not teeny and will self-propagate...

Onions tend to have multiple rings. Each seperate set of rings will produce a new plant. Todays commercial hybrids are developed to have single rings a highly desired trait especially when using for onion rings. Even so some of them will revert to multiple rings. Self propagation is pretty much restricted to topsetting onions and Allium fistulosum. Even potato onions and shallots require digging and replanting.