There is an old maxim in D&D: Never split the party. You usually hear this from the player perspective, in the context of survival advice. Just like a horror movie, as soon as you wander away from the party you are going to be the first corpse. United we stand, divided we are strangled by measles whilst taking a shit. Keep the magic users in the middle. Hi diddle diddle.
Of course there is a meta game reason to not split the party as well - the game runs smoothly when all the PCs are in one location, but as soon as they separate, the DM has to run each group through its actions separately and track time for each group. Temporal anomalies are a very real problem that you run into when you split the party - Bill and Ted spent eight excellent hours sleeping in the inn before going to the future, but in the meantime Beavis lit Butthead's fart on fire and burned down the inn. Usually a handwave back in time is enough to fix these sort of problems (umm, actually Bill and Ted, you guys didn't sleep through the night, you were awakened in the middle of the night to panicked commotion in the hallway and the smell of smoke, so what would you have done then?). If all the party members are each doing their own thing, at a certain point it would make more sense to stop playing as a group and start playing a bunch of interconnected one on one campaigns. Which actually sounds pretty cool, but it isn't really D&D as most of us understand it to be - a group experience.
I personally have no problem with splitting the party as a player or DM. The players in my new world campaign have made a lot of the traditional problems with party splitting obsolete anyway. All the PCs have a permanent telepathic link of unlimited range (this was created about two years real time into the campaign using the telepathic energy technology of the alien spacecraft that Tilia found on the moon) and can teleport to each other's side or back to the hovercraft as a minor action (they found a bunch of matched teleportal coins, pairs of matched gold coins that when activated open a portal between the two coins - each PC carries a coin linked to a coin carried by another PC, and each PC has a coin linked to a coin on the hovercraft, as well as coins to some other locations that the PCs have sprinkled around the campaign landscape).
While this solves many of the traditional problems of splitting the party, we have found ways to split the party into a more psychedelic fractal gamescape than I could have possibly imagined when this campaign began. For starters, we have been exploring the idea of splitting your consciousness into multiple copies for quite some time. I actually first introduced the concept in my (now defunct) Mutant Future game* when the PCs learned that a recurring villain, Julius Corple, had made multiple copies of his consciousness that inhabited a "space" called shadow, the "place" that energy "goes" when it flickers in and out of existence (although shadow is not a space or a place, and exists outside of time as perceived in the PCs universe, and energy particles don't so much travel through shadow as become it). Julius Corples' shadow consciousnesses could create seemingly magical effects by manipulating the way energy was structured in the Mutant Future reality, changing its form in shadow, outside of time. I have a unified theory of magical physics that I use in all my games regardless of system, and I allow exploration into and manipulation of magical physics outside of the normal D&D structure of spells, ritual magic and powers. My new world campaign is run using 4e rules, but of course shadow lies outside of the realm of 4e rules.
Fast forward to the present, four years into the campaign, and the last few sessions have been a "never split the party" purist's nightmare. One of the three main PCs did not even play at all last session, even though his player was in attendance and running two NPCs! Here is an outline of how the party was split up going into the beginning of last Tuesday's session:
Tilia A: Underneath the ruins of lost Eridu, between the first dungeon level of the temple of the moon complex and the surface, earthswimming with Hammer back toward the sacred lake to get a badly needed full heal from the holy waters (*not* psychically connected to the party's healer Beautiful Bob, who intentionally severed the link before going to sleep) .
Tilia B: [not active this session] surfing through deep shadow, retaining sanity because she is merged with a shadow dragon, in the middle of a subjectively centuries long mindfuck of a trip through the multiverses as the shadow dragon rides potential energy connections [note - Tilia split herself in two and Tilia B has already rejoined with Tilia A in Tilia A's timeline, but Tilia B is still an active game PC that we will revisit in future sessions to explore more about the nature of deep shadow and the way that energy is connected through the multiverses]
Hammer: Earthswimming with Tilia back toward the sacred lake to get a badly needed full heal from the holy waters (*not* psychically connected to Beautiful Bob, who intentionally severed the link before going to sleep). Hammer is a barbarian. He doesn't split himself up. Can he split something else up with his axe?
Beautiful Bob A: [not active this session] Hundreds of miles away in a cave in the swamp north of Siss Anor, in the middle of the horrific nightmares that are a withdrawal symptom of the psychotropic plants he consumed to aid in a ritual several sessions earlier. A Nur-Kubi shaman (kind of like a reptilian praying mantis anteater psychic vampire, the first sentient race released into the world by the snake man scientists) is siphoning off and feeding on the negative energy. Bob A intentionally severed his psychic link with Tilia, Hammer, Nur-Kubi, Zanninum, Beautiful Bob ∞ Beautiful Bob C before going to sleep, worried that the psychic energy that might be released in his nightmares could damage them (Bob A was supercharged with nightmare energy, having taken on the nightmares of the four million plus souls trapped in Mother Mind three sessions back). The session before last we advanced Bob A through several nightmare skill challenges, representing two full REM cycles of sleep, so we began last session needing to advance Tilia A and Hammer about 3-4 hours through game time before Bob woke up from his nightmares and re-established his psychic link with Hammer and Tilia.
Nur-Kubi the Cambion/FAKE Beautiful Bob [NPC controlled by Beautiful Bob's player, no psychic link to Tilia or Hammer] Guest bedroom in Lady Mirriam's compound, the old temple of the moon in the ruins of old Eridu. Nur-Kubi is assuming the appearance and demeanor of Beatiful Bob per Bob's commands. Nur-Kubi begins the session fifteen minutes in time behind Tilia A, Hammer and Zaninum. Lady Mirriam made a show of dismissing her handmaidens to the courtyard to watch out for any soldiers still angered by the party's actions of the day before (another story) and has shown Nur-Kubi/FAKE Beautiful Bob where her bedroom was and made it known that she would like him to visit her. Nur-Kubi is waiting a few minutes after his companions have settled into their adjoining rooms before strolling down the hallway. Nur-Kubi is behind Tilia and Hammer in time because the session before last, Tilia earthwalked through the floor of her bedroom and encountered some cultists of the Nameless One in the first dungeon level below and got in a fight. Hammer teleported to her side and they eventually killed the three lower level weretoad cultists and their higher level vampire leader, but not before sustaining serious wounds, expending a lot of powers and advancing their timeline past Nur-Kubi's.
Zaninum the Cambion [NPC controlled by Beautiful Bob's player , no psychic link to Tilia or Hammer] Just been spotted by the guards stationed around Lady Mirriam's compound (the old temple of the moon), was trying to stealthily make his way toward the sacred lake for a badly needed full heal after nearly being killed by an intelligent talking mace that could transform into a winged lion that he found last time while skulking around the ruins of old Eridu.
Curious George the hovercaft [NPC intelligent magical item hovercraft created by the party in dimension X using materials from that dimension] Circling high above the jungle, keeping an eye on things. Psychically connected to Tilia and Hammer (and usually to Beautiful Bob but not currently until Bob wakes up from his nightmares).
Beautiful Bob B [not active this session] surfing through deep shadow, retaining sanity because he is merged with a shadow dragon, in the middle of a subjectively centuries long mindfuck of a trip through the multiverses as the shadow dragon rides potential energy connections [note - Bob split himself in two and Bob B has already rejoined with Bob A in Bob A's timeline, but Bob B is still an active game PC that we will revisit in future sessions to explore more about the nature of deep shadow and the way that energy is connected through the multiverses - also Bob B is connected to Beautiful Bob ∞ and Beautiful Bob C]
Beautiful Bob ∞ [not active this session] Beautiful Bob split his consciousness up into a near infinite number four sessions ago in a shared dream with Maricanchi, an NPC dreamer from the future. Maricanchi will be an extraordinarily powerful dreamer and split into a near infinite number to show Bob the dreams of the past, present and future inhabitants of the campaign world simultaneously. [note - I gave Beautiful Bob's player an at will power called The Eternal Moment which allows Beautiful Bob A to connect with the infinite dreaming consciousnesses and learn more about the dreams shown to him by Maricanchi whenever he wants during play. The only answers that he can get are what the people in the past and future are dreaming, not necessarily the reality of what is happening in the waking world in the past or future]
Beautiful Bob C [not active this session] In the far future of the campaign world. One of the many Beautiful Bob ∞ dream consciousnesses has traveled inside the Dream Machine that Maricanchi and his triplet brothers are hooked up to in the future. The Dream Machine is a complicated piece of magic future technology that is somehow using the dreams of the three triplets to alter reality. Beautiful Bob C has managed to retain his consciousness while leaving the dream world and taking the form of a single particle of energy inside the dream machine. Two sessions ago Beautiful Bob C managed to break free of the regular energy routing inside the machine and did not go where the machine was sending his particle, instead choosing to explore the circuitry of the machine on his own terms [note - we will definitely come back to what Beautiful Bob C is up to inside the dream machine because the dream machine is directly connected to the mind of Manu Jablitu, the technomancer lich who the party would probably consider to be the main bad guy of the campaign at this point over the snake men]
* all three of the current players in my new world campaign were also players in my Mutant Future game. Those two games ran concurrently for quite some time and PCs from the Mutant Future game even briefly looked through a portal into my new world campaign but did not choose to go through it.