OK, not to throw water in anyone's faces, but.....here comes the splash
Assume a company commander goes down. The next highest ranking officer will immedietly assume command. If there are no officers left, then the highest ranking NCM will assume command.
As for control, that is something else. It simply means that the battle plan, as issued and ordered by the OC, continues to be implemented and monitored by the Headquarters, be it the CSM, signaller or whomever.
So, irrespective of people's opinions of how well (or poorly) OCs command their companies, and irrespective of people's opinions on who does what, if the OC drops, the 2IC is out, and the only officer left is 2Lt Ricky, two weeks out of IODP 1.2, then 2Lt Ricky commands the company. He is the only member left of the company who holds a commission, and as such, it's up to him.
Now, argue all you want about listening to advice, experience, etc; however, I riddle you this, Batman:
Suppose 2Lt Ricky doesn't know what to do. His OC is down, his defensive position is on the verge of being over run and there are casualties mounting. The CSM offers up that they should withdraw, to save the lives of whoever is left. Ricky nods and away they go. Suppose that the company was expected to conduct a delay or block or whatever, and by withdrawing, the enemy were allowed to break into the battalion rear area, or the enemy were allowed to escape a very well-planned Kill Zone, or whatever. The CO will be pissed, and he could care less what the CSM said. 2Lt Ricky will be the one to hang.