If Apple were to split iTunes I could see them replicating the app structure used on iOS devices. This would be in keeping with the upcoming Mountain Lion release and is separation of notes and reminders into their own apps.
So, I could foresee a new suit of apps.
iTunes - Just the store, same purple icon as iOS.
Music - The same orange icon as iOS, for music, podcast etc; organisation.
Videos - Again, same icon and feature use as iOS.
App Store - Consolidate the Mac App Store and the iOS App Stores together. Would allow for seeing truly ecosystem universal apps, along with those just for iOS or the Mac.
All of the above shouldn't be too difficult for users to adopt, as if they're familiar with iOS, the concept is already in place.
The only element that would the. Be missing would be syncing. For newer iOS devices this can all be done wirelessly, but a solution would be needed for the older iOS devices and legacy iPods. The reintroduction of iSync, used to communicate with all of the various programmes would allow the syncing to take place. Each tab referring to a different app, where it currently refers to a different element of iTunes.
If they really wanted to take things to their logical end, iBooks should be brought to the Mac, to be used for book organisation whilst a tighter integration with iPhoto would tighten the photo element.
It's only with the final two that I could see not being as simple, the four apps plus sync solution should work just as well orna windows machine as a Mac, it's only when working with Mac only software such as iPhoto where a compromise would be needed.
I agree with this. As you point out, Apple is working towards feature and UI parity between iOS and OSX. Separate iTunes, Music, Videos and App Store apps. The natural successor as the syncing and device management app is the App Store. Apps generally work on multiple different devices so this should be the central location to distribute them.