Not a complete answer, but look here
That's the US Navy organization in the Pacific as of May 1, 1945. Going to be a little different than your date as things were still expanding in 1943, and by May 1945 were pretty set.
Looks like 1st Fleet was all the Type commnaders under one roof, with 3rd Fleet, Fifth Fleet, and Ninth Fleet the operating forces.
A type commander then and now I think (the concept started in WWII I'm pretty sure) is a commander who "owns" a type of vessel. Sub, destroyer, cruiser, mine craft, etc. An operating fleet commander fights the assets. He doesn't take care of them. The type commander structure does that. Repair and maintenance, training, provisioning, alterations and upgrades, etc. All the housekeeping needed to get a warship ready to go up to the battle zone and fight is done by the type commander. Then he "chops" the ship to the fleet commander, and he puts it in a task force/task unit/task element to fight. If it gets damaged it's sent to the rear and the type commander owns it again unitl it's ready to go fight.
We still use this system today, modified by a unified theater command structure whichj integrates the navy, army, air force, Marines, and strategic assets into a chian of command which reports directly to the SecDef and then the POTUS, with the Joint Chiefs of Staff as advisors, but not operational commanders.
Looking at the Hyperwar document, it looks like the PhibForce COs rode the command and control ships, the AGCs. At least in May 1945.
< Message edited by Bullwinkle58 -- 3/27/2013 12:15:12 AM >