It's a very interesting topic, and it is rather difficult to assess how that works given the battle conditions, and the very low level of information given by CA.

I mainly (only) play MP, and my theory about morale is very different from the one hrvojej laid out.

In MTW, everything being equal (florins, even armies were looking alike), I would see a lot more chain rout than I see in RTW.
In MTW, a couple of units on flank, a dead general, and that was a mass rout, and if you could herd the mass rout well, you could trigger multiple armies chain rout. Actually, you did not even need the dead general, any hole in one army would trigger it; one unit start routing, therefore support morlae bonii are reduced, outnumbering morale penalty are increased, friendly routing morale penalty increase, and voila, everyone routs. The mechanism hrvojej describes in his first post is what happened in MTW.
In MTW, outnumbering penalty were so big that very few players would come with less than 16 units, even at low florin level. At low floring level, the main problem was that just massing a lot of units quickly was enough to cause a mass rout.

With RTW, it looks more difficult, and some of the players army choice make me think that, implicitly, some of the morale is understood to be different.
For example, I do think outnumbering morale penalties are much less than what they used to be: I see players taking less than 20 units quite frequently, and when playing with low denarii, playing with 10 units instead of 15 or 20 is a perfectly valid option: that was suicide in MTW because of the outnumbering penalty, it is not anymore, so I think this penalty has been tone down.
Flanking is still important, but I also saw complelty surrounded units fighting for a very long time.
I wonder if positional got different relative importance depending on unit status... Highly trained disciplined units caring less about flanking than warband. Actually you can make the same case about outnumbering... MTW had unit status (Elite or not), but I don't think it was as important as it is for RTW. Unfortunately, it is also rather difficult to assess the impact of those.

Also, being in formation might add to morale... or being disorganised might subtract from it. Units in good formation resist way better than the disorganised one that usually routs very quickly. Either it is a specific morale modifier, or the killrate is very high against disorganised units making them routing faster. To resist a rout, it is very important for units to be in formation!

Alternative assumption; it is very important for disciplined/ highly trained units, and not at all for impetuous one... hum...

Compared to MTW, one thing is sure, it's less forgiving; a tiny error, a unit misplaced, or too late, hence not in formation yet, and that unit is gone.

Louis,