This question of Kirk relieving Decker of command is an oldy. I find that the creators of Trek, being mostly ex Pacific theatre guys in WWII, had a natural understanding of navy culture.
Rules, regulations, and rank are one thing, er, three things. Anyho', uhh, However, any man who stands up and takes responsibility might be bending or breaking one or all of the above but that's doesn't mean they can't. Like "the Caine Mutiny" (classic oldy film kids), this adventurous ep of Trek was on full Horatio Hornblower mode. The conflict between Decker and everyone else was the story and, I suspect, this is why Decker was the ONLY example of a commodore in command of a starship (excluding the war games lead by Commodore Bob Wesley in The Ultimate Computer).
It's hard to say if Kirk overstepped his authority when he was the authority on the big e. But it's just as hard to say Decker was indeed following regulations when he took command, as he insisted. After all, he was in no condition to command and certainly took advantage of regulations while ignoring his own shocked and delusional state of mind.
Ultimately, whomever is in command on any ship, even today, is the person who is given command
first. Kirk was responsible for the enterprise, not Decker. I think star fleet legal would see Deckers taking command as crass if technically by the book. After all, Kirk wasn't dead, he was still in command but merely out of communication temporarily. Decker clearly overstepped.
imho.
