Overall Structure of Producing Physical Firm

For a physical firm that does not run a purely flat, hedged book, I’m honestly a little lost on the overall structure/strategy – basically – how are traders initial positions established?

My understanding is that a BP, Xstrata, Shell, etc. has its E&P arm that drills or mines for the commodity. From here is where I’m unsure of how the relationship progresses. Do they “sell” it to the marketing/trading arm? How is ownership transferred and how is it accounted for?

Also, if this is even remotely similar to how it’s done, how are quality differentials allocated? (In my examples my quantities, prices, etc are obviously going to be small and simple)

Trader A:
1000 bbls SGC @ Atlantis
1000 bbls WTI @ Midland

Trader B:
1000 bbls SGC @ Atlantis
1000 bbls WTI @ Cushing

So are these traders “given” this oil to market as well as some cash/credit from which they derive their strategy and formulate the positions they actually want to take? I know this is extremely elementary but this is a fundamental that I don’t understand.
Anyone that can help this would fill a HUGE gap in my understanding.