I too have wondered about the size/thickness of De Lorenzo's over the past few years.
I found a picture on Flickr that puts a new perspective on the pie, definitely not what I had imagined. It is amazing what happens when you see a picture from a different angle.http://farm1.static.flickr.com/150/370215542_3335fca1cd.jpg
Obviously the pie has cooled off but you can still see a little better how it looks. Very thin with a larger, flat, outer rim.
The 'tomato pie' seems to get a little different as you head into Philadelphia, for ex: http://www.conshybakery.com/
has tomato pie on their products page (as well as many other yums) but it seems to resemble a "grandma" pie or a basic sicilian more than what De Lorenzo's serves.
But the humble tomato pie has multiple personalities. A "bakery-style" version shows up in Italian bakeries across the region, notably in Manayunk, the northwest suburbs and the Far Northeast. It is a large, rectangular baking sheet of hand-rolled, yeasty crust, a rich, thick, chunky tomato sauce and sometimes a light sprinkling of grated cheese on top. Sold at room temperature, it's a staple for hundreds of tailgaters at every Eagles home game.
A tiny sliver of the Northeast along Frankford Avenue is home to a different kind of tomato pie: Round dough topped with slices of mozzarella or provolone (or both), followed by a spicy, garlicky tomato sauce. It emerges from the oven bright red, thin and crispy, with a room-filling fragrance.
So it seems as if there are two quite different things in the same region defined as "tomato pie"
1. "De Lorenzo's Style" tomato pie, built more like a typical pizza - simple toppings, defined by the bright red sauce topping the mozzarella cheese.
2. "Deli/Bakery Style" tomato pie, almost certainly square, good to eat either reheated or at room temperature.