Now I know this was explored to some extent in the
"The Death of Göring and the Victory of the Luftwaffe" timeline, while an interesting timeline in it self I disagree with quite a bit of it, particularly the impacts it would have on the German rearmament as Hjalmar Schacht had problems with the rapidness of it, which was why Göring was appointed Plenipotentiary of the Four-year plan.
So hypothetically speaking say Göring dies from a disease, accident or through some other non-violent means sometime in -36 or -37, who takes over what? The most important would be:
President of the Reichstag
Reichminister of Aviation
Commander-in-Chief of the
Luftwaffe
Plenipotentiary of the four-year plan
And what would the effects be of those who have taken over?
For instance if Wolfram von Richthofen takes over as C-i-C of LW, that would kill the Ju-87 as he thought it was a waste of resources. That and the sacking of Ernst Udet, as v.Richthofen detested Udet.
Would Fritz Todt be able to take over at that point as PP of the 4YP ? A sort of proto- ministry of arms and ammunition? And how would he do at it at this point?
I'm planning on doing a TL about just this EXACT scenario. There is a metric ton of research involved, so I'm years away at this point. As it is I've already read about 100 books and counting preparing, not to mention about 200+ articles from Jstor. I'll add my two cents and feel free to take whatever can help.
The president of the Reichstag would probably be Hess, Milch at the RLM, Wever for CiC of the Luftwaffe, and Fritz Todt for the Four Year Plan.
CoS of the Luftwaffe is tough. I'm planning on Wever bringing back Helmuth Wilburg for the job, as there really is no one that can do what Wever did but him, and Wilburg was even better for the job than Wever, but Wilburg was half Jewish. Goering kept him around due to his immense skill, just as he did Milch. Apparently Wever and Wilburg were very much on the same page, so I could see Wever doing this, even with the potential political blowback.
Wever and Wilburg means that Richthofen would stay in the technical department, but Udet's influence would still result in the Ju87. Udet would be on the way out though, to some non-influential position, like chief test pilot, where he would flourish and actually be useful.
With Richthofen remaining, Walter Wimmer would remain his boss. That is VERY good for the Luftwaffe and Germany. Loeb would stay in technical production instead of being taken by Goering to the 4 year program and Milch would have total control over Luftwaffe production, meaning the Luftwaffe avoids its failures in the He177 and Me210, saving tremendous resources and ensuring the first operational strategic bomber Staffel in 1941.
Also the Bf110 is probably nixed by Richthofen and his pet project, the Fw187, is produced instead, though with a 1 year delay over the Bf110. That means the operational FW187 Staffels appears in 1940.
Fritz Todt and Albert Speer (his OTL deputy) would get the 4 year program and cause major problems to the Nazi party, as Todt was technically brilliant and Speer political ambitious. It'd be brutal as these two topple their rivals left and right, especially as they were both Hitler favorites. The 4 year program and the German economy would be far better organized and party hacks would get gutted in the fight for control. Expect things to be centralized under Todt, with his hatchet man Speer doing the dirty work for him. Even the Wehrmacht would find itself shut out of production interference, which is a major boon to production.
Basically the German economy is ready for war in 1939 far more so than in OTL, thought still developing. Lots of the economic pitfalls that occurred OTL before 1942 will be avoided, so that by 1940 the baseline would be like 1942. After that production ramps up quick, outpacing Britain in 1939, and perhaps the Soviets by 1943. Certainly issues like the failed economic mobilization of 1939 will be avoided (Goering hadn't completed a mobilization plan for industry or labor by 1939, which meant that no one knew what to do when war happened), as will the 'war of all vs. all' that resulted from economic command fragmentation under Goering, which was only OTL sorted out by Todt in 1941.
I would say that by mid-1940 Milch could be producing 25,000 aircraft a year, with expansion topping over 60,000 a year by 1942-1943. Depending on how things play out in the war, I have my own ideas about that, Britain could be knocked out in 1941, but if not the Western Allies are going to take a lot longer to win air superiority over Germany.
The East is going to be nastier too, as Germany wages a much more effective war with Wever in command and the economy properly organized. Assuming the same political mistakes are made and Germany doesn't knock out Britain, then the war could well last into 1946 or 1947 in Europe.
If Britain is knocked out, which IMHO is an honest possibility, then Germany doesn't lose the war.