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:
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.