First of all, I don't understand anything about combat width. I think you mentioned a battalion-width conversion factor in your last post but I can't remember. How does width actually work on the map though? Does each little unit of territory (forget what they are called, provinces? the ones that make up States) have a set width?
Width doesn't have anything to do with the campaign map. You can occupy each individual tile with 2-battalion divisions and it counts as having troops there just as much as having a 40-w monster division there.
Width is all about the combat system. When two forces engage in combat, they initially have only 80 width to deploy their forces. Thus, it's best to have armies comprised of divisions that are evenly divisible into 80. If you have three 30-w divisions, only two of them will deploy initially because all three of them would be 90 width.
Now, width comes from the number of battalions in the division. Larger divisions - with better stats - have larger width. Thus, if you've got two 30-w divisions fighting against two 40-w divisions, the 30-w ones will intrinsically be weaker because they're smaller.
40-w divisions are the largest size that can be divided evenly into 80 width, thus they are the most efficient means of massing combat power in the initial phases of a battle. Two 40-w divisions contain the same amount of combat power as four 20-w divisions, but due to the targeting mechanics in HoI4's combat system, the four 20-w divisions will all be shooting at randomly chosen things, which may result in a dispersion of combat power. The two 40-w divisions will be guaranteed to be shooting at only two different targets maximum, meaning that they are slightly more efficient when using their combat power offensively.
Defensively, 20-w divisions are fine, because you're not trying to concentrate your firepower and break through immediately, you're just trying to outlast the enemy and make sure that you cover all of the provinces you need to cover when defending. 10-w divisions are also fine, depending on context. Really, the 40-w thing is only useful in an offensive context when you are trying to win the initial fight as rapidly as possible by massing the absolute maximum amount of combat power possible under the 80-w initial engagement system.
Larger divisions also consume more supply, which is calculated based on the number of total battalions in a given region and those battalions' supply requirements for the mission they're currently executing.
Second of all, how does one determine where one's captured equipment etc goes? Is there a screen I'm missing other than Logistics, Production, Recruit+Deploy which enables finer control of what equipment goes to what units?
Take a look at the logistics tab. As you know, it shows all of your equipment divided up by type, along with how much of a surplus or shortfall there is compared to the amount of equipment that your currently-deployed divisions require. Mousing over individual categories (like Medium Tanks, for example), will show more of a breakdown by type; you can tell which pieces are captured based on their names (i.e. if you're playing Germans you can assume that all the Char B1s under the heavy tank tab are captured).
The game automatically tries to update your divisions with the most recent available equipment. You can see the equipment used by each division individually by selecting the division. This also works for air wings - you can see which are using, say, Bf 109Es, which are using Fw 190As, and which are using captured MS.406s.
You can also kludge your way into a list of all of your equipment by going to the diplomacy tab and offering a Lend-Lease agreement to somebody. This will allow you to page through all of your equipment by type and number.
EDIT: Some of this may not work if you don't have all of the expansions. If you don't have everything up to WTT, I'm not sure how equipment management differs. Sorry!
Third of all, how do I change one division into another kind of division (assuming this is possible)? As Germany I start with a bunch of these useless Leichte divisions and I wanted to just make them all into normal Panzer divisions.
Select 1 or more divisions. There should be an icon with arrows on it that allows you to change the template of that division. The game will show you the change in equipment use from one division to the other and will let you know if you don't have enough equipment to make the change. (You can still make it, but all of the equipment that you don't have won't be there until you accumulate enough of it to reinforce the division - with an associated reduction in combat power for the division.) It will take some time to reinforce the division with the new equipment, and it will lose some experience levels based on how big of a change it will be.
Fourth, why is mechanized infantry only viable starting in 1942? I researched the halftrack tech in 1939 as the Germans and started filling out my armored divisions with mechanized infantry instead of motorized, and also created a Panzergrenadier division with 12 mechanized infantry battalions. I'm also using motorized divisions comprised entirely of motorized infantry with self-propelled artillery in support, with the intention of phasing them out and replacing with the Panzergrenadier format.
It's not "only" viable starting in 1942, but that's the point at which you're most likely to be able to make the change for most countries based on opportunity cost. Many players wait until MECH II because they don't have space for an additional production line that early and because MECH I, while a hardness upgrade over MOT, is a more significant speed reduction than just going to MECH II. But you certainly don't have to wait for MECH II if you don't want.
MOT and MECH units to hold flanks can work quite nicely. In KR games as Russia, for example, I often invest heavily in 20-w full-MOT divisions for encirclement purposes, taking the place of the LARM units that vanilla HoI4 players often use, because of the difficulty of researching LARM techs thoroughly in time for the Real War, whatever that happens to be. They work nicely at holding flanks and breakthrough corridors, as well. Full-MECH divisions are good ideas if you're facing enemy armored attacks on the flanks of your breakthroughs, but are otherwise probably unnecessary compared to MOT. You can use them to push if you like, but if you've got your 40-w armored divisions rolling, extra pushing power is probably unnecessary.
This is helpful, thanks. I just researched Jagdpanthers but I guess I won't actually use them.
The secret to comedy is timing.
Can confirm - I saved before beginning my western campaign as the Germans, and had to reload that save because I forgot to focus my air power on Benelux and Northern France rather than the North Sea and north/west Germany. Without any air cover my units couldn't even beat the Low Countries' units, but things went a lot better when I had air superiority.
Yeah, it can get pretty embarrassing if you don't set up your air wings properly.
