Collie: it needs to be deep enough to accommodate the root mass and it still might be top heavy . I've seen some weird set ups. One of the gardening magazines you get for free from the hydro stores like, "MAXIMUM YIELD," had an interesting article last year about people, (I think in Japan), growing on an absorbent film that they evidently flood and drain.
At school they encourage us to try new things and one of the most bizarre set ups I've seen recently was a relatively shallow plastic storage tray like you see at places like Target and Walmart put to better use. I would guess it was probably designed for the safe storage of papers or photos or maybe even a layer cake. It was only about three or four inches deep and about the size of a baking pan. The bottom was originally clear plastic with a red lid but he'd painted the clear part blue to keep out the light. It had about six or eight holes in the top and the tiniest net pots that I've ever seen with little rock cubes in them. They weren't much bigger than my Aerogarden's planting baskets. They were stuck into the top of the lid and he'd set up a long air stone in the middle to move the nutes and add oxygen. The plants were under a couple of CFL's and they looked happy. He called it his nursery.
He was talking about putting in a couple more holes in the end and recirculating his nutes with a little external pump. That sounded too involved for such a little grow and unfortunately I've lost track of him since the semester break so I don't know if he ever did it. He had a number of tiny plants, maybe 6 inches tall at that time growing in it but it seemed to work fine. What he'd do after they got tall enough to want to fall over I don't know. I'm guessing that when his little babies start really sucking up the nutes it might be a problems staying on top of his grow but this might be something for you to think about. He only had a space about 2' tall to grow in over his desk. I hope this helps. HSA