What are they parameters of brov am hadras melech? is it a requirement or a hiddur? does it apply equally to men, women and children? why does it not seem to apply to zimun (preferable to split into multiple groups)?
Perhaps by Zimmun you are referring to the concern that the group will not hear the leader. Recall that Zimmun originally meant that the leader said all the blessings out loud and everyone fulfilled their obligation by listening. Thus if you couldn't hear the leader in a big room then you did not fulfill the biblical obligation of bentching.
(Note also that generally speaking, you cannot break up a minyan for zimmun because then you lose the opportunity to say the zimmun with God's name. You can however break up a larger group into smaller groups so long as you don't switch from a zimmun of 10 to one of 3 or from one of 3 to alone. (Shulchan Aruch OC 193:1))
Here is a relevant piece of the Shulchan Aruch there which perhaps you are referring to:
ומיהו אם היו רבים מסובים יחד ואינם יכולים לשמוע ברכת הזימון מפי המברך, ואינם רשאים ליחלק לחבורות של עשרה, מפני שיצטרכו לברך בקול רם וישמע בעל הבית ויקפיד עליהם, יכולים ליחלק לחבורות של ג' ג' ולברך בנחת כדי שלא ישמע בעל הבית, וזה טוב להם ממה שלא יצאו ידי חובת ברכת זימון, שהרי אינם יכולים לשמוע מפי המברך.
However, if there was a large group together and they cannot all hear the leader and they can't split into groups of 10 because the host of the meal will hear and [be offended], they should split into groups of 3 and bentch [with a zimmun] in hushed voices so the host will not hear; [even though they will lose out on saying the zimmun with God's name] it is better for them [to split into threes] than to not fulfill there obligation in bentching because they cannot hear the leader.
This is the only reason I can think of that it would be preferable to split into groups. Otherwise I imagine Berov Am should apply.