Why not leave some there and take some to grow out for bigger yields? Left to its own devices, garlic will divide and spread like daffodils, but the bulbs will be small and won't multiply as fast as when they are planted several inches apart and pampered. The bulbils will start new clumps. The main risk you run is disease, but if you're not adding new Allium material that risk may be small. Letting the scapes go does reduce bulb size in most cases, but if you make sure they have enough nutrition their health shouldn't suffer. Just treat them like any perennial bulb.

If you do want to grow big bulbs, you should plant them in the fall. Timing, depth, etc. will depend on your climate and conditions. Pick up a good book like "The Complete Book of Garlic" by Ted Meredith and you'll have a great foundation.

I was going to add that re: garlic that "does not top out." If you mean it doesn't form a scape (flower stalk), that could be shade or other conditions, or it could be a non-bolting variety (commonly called "soft neck"). Those varieties still form a divided bulb but often don't form a scape.