Toobworld and The Tooniverse are two mega-dimensions, subsets of the TV Universe. All of the TV cartoons ever broadcast co-exist in The Tooniverse, while Toobworld is the general depository for live-action TV. Toobworld (aka Earth Prime-Time) has thousands of alternate dimensions, thanks to 'Sliders', in which TV shows that don't quite fit with the overall schematics of Toobworld can be placed. (This would include TV shows that are remakes of original series, or shows in which the President of the United States is not the same as the one in the Trueniverse.)
The Tooniverse has a few alternate dimensions as well, for those rare times when a cartoon just can't logically fit in with the rest of the toonic output.
Sometimes, characters cross over from Toobworld into The Tooniverse, but for the most part, it would be the residents of the cartoon dimension who make the journey across the vortex which separates them.
Three examples would be the animated Superman visiting the live-action Metropolis in the American Express blipverts, Daffy Duck applying for a job at Winfield-Louder at the beginning of an episode for 'The Drew Carey Show', and Homer Simpson crashing down into the set for the 'Live With Regis and Kathy Lee' program. (That happened in one of the Halloween editions of 'The Simpsons' and would be a great example of cartoons that have to be relegated to an alternate Tooniverse.)
The possibility exists for cartoon characters to wander into any live-action series, as the rules of Toobworld should apply to all TV shows. However, as is the case with the living puppet people, it's kind of an unspoken rule that we don't want to see this happen to most of the TV shows out there. Otherwise it destroys that willing suspension of disbelief that what we're seeing in a live-action TV series is actually happening.
How could we as the audience continue to be drawn into the world of 'Heroes', which is already precariously teetering on the edge of believability with its many super-powered humans, if suddenly one of those characters was pen and ink, not flesh and blood?
The movie "The Last Action Hero" was similar to the Toobworld concept in that a young boy ended up in a movie universe that combined many different genres, cliches, and characters. It had plenty of faults anyway which were subject to ridicule, but I remember that many of the reviews singled out the appearance of a cartoon cat named Sgt. Whiskers who used to be the main character's partner. I guess if there was any semblance of believability at that point, it went out the window with the appearance of the Danny DeVito-voiced feline.
The same thing would hold true if Bugs Bunny suddenly popped up out of the remains of the Hatch, having taken a wrong turn at Albuquerque. Once he saw Jack and said, "What's up, Doc?", 'Lost' would probably lose even its most dedicated fan-base.
That's not to say it can't happen; just that we shouldn't be able to see it happen on-screen.
Off screen, perhaps it happens all the time, and we got an indication of that last week on '30 Rock'. At one point in the episode, Jack Donaghy was listing all the hip-hop and rap artists who were going to be appearing at the Source Awards, among them Ridikkulas (a play on the name Ludakris) and MC Scat Cat.
MC Scat Cat was Paula Abdul's dance partner in those otherwise forgettable music videos from probably twenty years ago. Now, looking at the shout-out from the expected audience reaction, it was meant to be a joke and Tracy Jordan even noticed that Jack had mentioned a cartoon character ("Whuuuh?").
But within the reality of Toobworld, who's to say MC Scat Cat hadn't crossed back over to the world of live-action TV once again to appear at the Source Awards? Just because we didn't see it happen doesn't mean it didn't. We never saw Khan Noonian Singh meet Pavel Chekov on 'Star Trek', but we know from "The Wrath Of Khan" that they did. (My favorite example of that!)
So the integrity of '30 Rock' - funniest new sitcom on the air this season! - is upheld, while at the same time the fantasy world of Toobworld gets a new game piece.
Let's crack open a bottle from the Donaghy Estates to celebrate!