Suppose I have many pounds of fat to render. (Sometimes people have 100 pounds!) How can I do this efficiently?
Should I use a pot on the stove, a slow cooker, or the oven? How many pounds should I render in each batch? Do I need to add water?
Unless you've got industrial type equipment, I wouldn't do more than about 1-1.5 lbs at a time. Here's a hint, cube the fat (1 inch cubes) and then partially freeze it. 45 - 75 minutes or so in the freezer will give you fat you can handle without it melting and that can be coarsly ground in a food processor or meat grinder without making a gross mess. Some people add water, I wouldn't. Just keep the flame (or burner) very low. Use a heavy pot, preferably cast iron. If you do it nice and slow you should get cracklin and tallow that barely needs to be clarified, or not at all. Figure about an hour on the low end up to two hours for the fat to completely render.
If I was to try and render the huge amounts of fat you have hinted at I would do it in water. You'd need a suitably large pan obviously to fit the quantity needed.
Most of the sediment will end up on the bottom of the pan but some may get trapped in the top layer.
Well if you think about when you're making a meat stock for example, you simmer the contents for hours. Fat floats to the top, you ladle it out then pass the result through fine sieve. All you're trying to do it the same but instead of a tasty bottom stock you want the fat.
This method is more likely to give a pure, clean and untainted fat. Roasting or frying is going to cause burnt bit's of meat etc, the flavor of which I'm sure will be present in the resulting fat. Also any smoke cause by the roasting method is again going to taint the end product.
Regarding the water at the bottom, an untested thought/thory would be to add a couple of pig trotters to the mix. The resulting gelatin will in theory set the water solid at the bottom also grabbing all the sediment's and other juices. Then allowing you to turn the entire pan over heat slightly with a blowtorch and remove the pan. Then with a warm knife slice the bottom(now top) layer off to remove all the unwanted stuff.
I see no reason why this method couldn't be done on an infinite scale only limited by pan size.