When those tops form on Elephant Garlic, are they supposed to be left there to flower & go to seed, or should they be picked off?

No, definitely cut the seedheads off. This goes for most crops.

Why?

Well, it helps the plant put more energy into the bulb production rather than producing seed.

So, you are saying that if you want seeds you leave the top alone & harvest the seeds after the top dries, & if you want a bigger bulb you cut the top off. Either way, you can still use it for cooking... right? Does the bulb make more baby bulbs?

The bulb that you harvest will be comprised of several cloves. You break up the bulb into the individual cloves and plant them like you did this year. Each clove will yield another bulb with several cloves.

I'm not sure about elephant garlic since it's technically a leek, but if it is like true garlic, the scape will produce a top with baby bulbs. You can plant the baby bulbs, but it will take 2 years of growing to get a full sized bulb. You can still use the 1 year old plants for cooking, but they won't be the same size. I even use the baby garlic bulbs for cooking.

Last year I planted (2004) 50 cloves to experiment with trying to properly grow garlic. We bought seed garlic ("music" is the variety-hardneck). I prepared the soil in September and planted in October, 8" on center one straight row. They were mulched with straw and let to winter over. They did start to sprout before the ground froze and started growing again in March (2005) right through the mulch.When the scapes came along I had the same question cut or not to cut. Definitely cut! The plant will put it's energy into the bulb rather than producing a flower head. The scapes are great to eat fresh, steamed, sauted, flavor olive oil. Last October we put in approx. 1500 cloves or 40 lbs. worth.
it is growing fantastic. I did put in 10 elephant cloves for this years harvest (as big as a baking potato each). We have gotten our seed cloves at the "Hudson Valley Garlic Festival" in Saugerties NY (good take).
ranger