From: Denver Colorado
Priority is self-contained.
In other words if you set Army Group South to 5 and Sixth Army to 0 and 29 Corps to 2, during the phase in which SUs are shuffled, the only thing that matters is that specific HQ's setting at that moment. They only think for themself, and no one else.
So in the above settings, excess SUs in 29 Corps are going UP one level to 6 Army. However, if 29 Corps does not have 2 of EACH TYPE of combat SU (more on this later - it's very important), then it 29 Corps will PULL down SUs from 6 Army. The only thinking entity here is 29 Corps - 6 Army isn't influencing the decisions of 6 Army's pull request. Either 6 Army has stuff 29 Corps needs, in which case it pulls. Or 6 Army has nothing 29 Corps needs, and no pull happens. Note that it is possible to both pull and push given the right circumstances. For example, if 29 Corps had 2 of every type of SU except Anti Aircraft (which it has 3) and Jagdpanzers (which is has 1) then it can both PUSH the Anti-Aircraft UP (to 6 Army) and PULL a Jagdpanzer from 6 Army (assuming first that it has one).
Now, let's assume for a second that Army Group South has all the SUs in the world, at setting 5 as above. 6 Army has zero SUs (and setting 0) and 29 Corps has setting 2 as above. Now let's assume 29 Corps has zero SUs in it.
In this example, 6 Army will never get SUs to pass down to 29 Corps. Because 6 Army is set to 0, it will not pull anything down, therefore, 29 Corps will never have a selection to draw from.
Where this gets tricky is in knowing what each "Type" of SU is. I can speak better here to Germany than to the Soviets, just from memory of the names and types.
In German SUs, "Gun/Howitzer/Artillery" are all one type
Nebelwerfers (which are a type of artillery) are a separate type.
Heavy Artillery and Heavy Nebelwerfers are EACH a separate type still.
Stug is separate
Jagdpanzer is separate.
All anti aircraft SUs are of a single type
Note that pioneers/sappers (soviet) never move on their own, you have to move them manually.
So you can give yourself a serious SU problem when you set higher tier commands to hold a lot of stuff. In practice, I find it a very bad idea and practice. You can end up with an Army Group having 5 howitzer/gun/artillery, AND 5 Heavy Artillery AND 5 Nebelwerfers AND 5 Heavy Nebelwerfers, and that's a nightmare to re-sort. With a setting of 1, you'll get one of each of these, and that's not nearly as problematic.
I occasionally set certain Army HQs to 1, and same for Army Groups. OKH is always set to 9.
Spring 2017-Playing: Hell's Highway, Advanced Squad Leader,
Reading: Kampfgruppe Walther & Panzerbrigade 107 (Magnificent). Lots of Osprey stuff.
Rulebooks: ASL (always ASL)