OK, let's introduce the US Army Armored Division, 1944-1945.
First a note: I'm still not entirely happy with this formation.
The division is radically different from the AD of OTL.
The division has an HQ, three Combat Commands (A, B, R), Division Artillery, (all four of the above effectively brigades), a mechanized cavalry squadron, engineer combat battalion, self-proppelled AA battalion, medical battalion, maintenance battalion, transport battalion, and support battalion (QM, signal, MP, etc.).
Combat Commands A and B are identical, each having an HQ & HQ company, heavy tank battalion, armored infantry battalion, assault gun company, armored engineer company, medical company, and support company. They are intended to be breakthrough and exploitation columns with attachments as needed from the division base.
Combat Command R has a medium tank battalion, mechanized infantry battalion, tank destroyer company, armored engineer company, medical company, and support company. It is intended to be a mobile force that will move rapidly to a key objective and dig in to hold it against an expected counter-attack, in support of CCA and CCB, again with attachments as needed from the division base.
Division Artillery is essentially the same as an infantry division's DivArty, just with SP guns. There are three FO teams per battalion, each with a halftrack instead of the infantry division's jeeps. Halftracks are generally used as command vehicles instead of jeeps, 3/4 ton trucks, etc.
A heavy tank battalion has 68 M26 tanks in three companies, each with four platoons of five tanks, plus two HQ tanks. The battalion has an HQ company (SP mortar platoon, recon platoon, signal platoon), plus a support company (maintenance, recovery, transport).
A medium tank battalion is the same as that found in an infantry division.
The armored infantry battalion has three companies of infantry mounted in M39 APCs. This vehicle did exist IOTL, though it was not used as an APC during the war, plus HQ and weapons companies. The rifle companies each have 22 vehicles; two company HQ, three platoons of 5 each, and a 5 vehicle mortar platoon. The M39 carries a nine-man squad, plus the driver. The weapons company has three AG platoons, each with three modified M3 tanks (the turret is replaced by a 40-tube 'calliope' rocket launcher but the hull-mounted 75mm is retained), plus a scout platoon. The HQ company has signal, maintenance, and transport platoons. This is the unit I took out all the stops for. Its mission is to accompany tank units, dismounting as close to objectives as possible. It can also lay down a huge amount of area-effect firepower.
The mechanized infantry battalion is similar to the armored infantry battalion, but mounted in halftracks instead of APCs. Its rifle companies also have 22 tracks, but rifle squads are a full 12 men, and each company has a pair of towed 57mm ATG, a pair of 60mm mortars, and six HMG teams (two per platoon). The weapons company has three 81mm mortar platoons (three tubes each) and a scout platoon. The mechanized infantry battalion is intended to move rapidly to the edge of battle, or to seize and objective, and dismount to assault or defend it on foot. It has less total firepower than the armored infantry battalion, but far more dismounted firepower.
Assault gun companies have 20 M4(105) tanks plus an HQ element.
Tank destroyer companies are the same as found in the infantry division (M36 TDs).
Armored engineer companies have two halftrack mounted combat engineer platoons, an Armored Vehicle Launched Bridge platoon (2 AVLB with 36 ton bridges), a support platoon, and an HQ. They are intended to assist mobile columns in crossing and destroying small obstacles.
The division's combat engineer battalion is truck-mounted and primarily intended to create defensive works or dealing with larger obstacles. It has three combat engineer companies and a construction company (the same organization with only minimal changes is found in the infantry division combat engineer battalion).
The mechanized cavalry squadron has three mechanized cavalry troops plus a HQ troop and a support troop. Each cavalry troop has three platoons, each with three M8 armored cars and three M20 scout cars, plus a light tank platoon with five M5 tanks and a company HQ with two more M20's. The HQ troop includes a pioneer platoon (halftrack mounted; a cross between a rifle platoon and an engineer platoon) and a mortar platoon. It is intended to find the enemy, eliminate enemy reconnaissance units, and screen the movement of the division. The 37mm guns of its M8's and M5's are no match for real tanks, but quite sufficient to destroy enemy armored cars and softskin vehicles.
The SP AA battalion is almost identical to OTL. Support units are similar to OTL, though somewhat larger as the division as a whole is larger. (OTL: ~11,000 + 2,000 standard attachments, TTL ~16,000).
For comparison, OTL the standard armored division had three medium tank battalions, three armored infantry battalions (halftrack mounted), three SP 105mm howitzer battalions, a mechanized cavalry squadron, an armored engineer battalion, and a bunch of support units. The combat units were also organized rather differently. The division had only two Combat Command HQ units, though doctrine called for a CCR anyway. A third CC HQ was usually attached in theater to provide a commander and staff for CCR.
The OTL TO&E has been criticized for everything from insufficient infantry support to being too large to control to lack of organic artillery. I've tried to provide a formation which is tough enough to take and hold objectives on its own while still being small enough to control as a single unit. To do this I've invented some vehicle modifications (the M3 never had a calliope fitting AFAIK), pressed other vehicles into roles they weren't used for (M39 as an APC instead of a towed gun prime mover), and put some vehicles into wider use (the M26 tank and the M12 155mm SP). This unit would require much more transport to ship it anywhere, but hopefully would require less sustaining support due to lower losses.
I welcome suggestions.