Question regarding how Supply is calculated

[Crossroads]

I think the chain works from the top down as listed in your OOB file. Example a division hq supplies regimental hqs beneath it(and battalions or companies attached to it). They in turn supply Battalion hqs beneath them. Battalion then supplies company or platoons beneath them. Manual explains the benefit of keeping company units within range of their hqs. So, every turn division hq will check with base supply if it fails it is out of supply wether it moves or not. Regiment will check with division and if it fails it will check with base (I think). Battalion should work the same way. Platoons will check with battalion using the company adjustments. If they fail they have no where else to check and will remain out of supply.

One more time... (Bold emphasis by me)

I have put logistics as a key theme for my current battle (The "A Legend Is Born DAR" I am doing at the mo).

Can someone verify to me (one more time please, I am having a hard time trying to figure the whole logistics chain out...) the chain-of-command logic regarding the case where a lower-level HQ is making a supply check from a higher-ranking HQ, but the higher HQ is out of supply.

Is base level supply then checked, or not?

Case 1) If Regimental HQ is out, Battalion HQs still try the base level. Yes or No?

Case 2) If Battalion HQ is out, regardless of Regimental HQ status, the companies are out of luck. Yes or No?

Case 3) Does the Company command post (1st platoon) need to be In Supply, for the other platoons to receive Supply from a Battalion HQ, or is it enough the company remains close enough to Coy CP for the Battalion HQ to do its magic? Former or Latter?

Lots of questions, sorry... Thanks!