The Rules of Dragon Ball Z:
Probably the best way to introduce Dragon Ball Z is by the basic"'rules" of the universe. Of course, these aren't Toriyama's rules, they are my rules, derived from the general look and feel of the manga.
Most of the action of Dragon Ball takes place on "Earth". Not "our" Earth mind you, but an "Earth." The impression I get from reading the manga (and seeing a few official maps) is that the planet isn't very large (it seems smaller than Earth) with a single large continent and a lot of islands (repeat: a lot of islands). The terrain ranges from hot jungles to wide open plains to frozen tundra to forests. Animal life is very varied, with dinosaurs and other large creatures sharing the landscape with more "modern" animals. There aren't that many countries either; in fact, the planet seems to be under one single government run from a central capital.
The population of the Earth in Dragon Ball Z is highly varied. It is mostly humans, with a small number of anthropomorphic animals, and a scattering of monsters thrown in for good measure. In general, there is no real difference between humans and anthropomorphic animals, except for looks. As for monsters, Toriyama introduced werewolves and vampires early on, but those seemed to be used more for their humor value than as serious threats. In some of the early Tenkaichi Budoikai, Goku fights such beasts as a huge wolfman, a dragon, and other foes. Most of them seem very strong and powerful, but not very quick (or smart).
There are alien races in the universe of Dragon Ball Z. The two most prominent are the Saiyajin and the Namekjin. Naturally, there are others, such as Freezer's race, as well as a whole swarm of humanoid aliens that appear only as background filler and grunts. Along with the aliens there are spaceships and space travel, but the idea of actual interstellar empires and all is never examined.
Aside from the aliens, there are a few "gods" as well. There is: Shenlong, the dragon god, who can grant wishes; Mr. Enma (or Enma-sama) the man who guards the entrance to the Underworld; Kaio-sama, one of four Kaios who monitor the four quadrants of the galaxy; and Kaio-shin, one of the gods of the Kaios. These characters (and the others like them, such as Madoshi Babidi and Buu) are all fairly powerful, but in general are rather benevolent (or, at least, not trying to kill our heroes).
Places of note in the Dragon Ball Z world:
Kame House: The home of Kamesennin Mutenroshi, this house is located on a very small island in the middle of the ocean. Kamesennin lives there, as well as a large turtle, Kulilin (until he marries #18), and for a short time, Kushami. The house is often used as a staging ground by the cast. The Z-Fighters will often gather there to plan their next moves while fighting some powerful enemy.
Karin's Tower: This very tall and very skinny tower is located in the middle of a thick forest. Karin-sama (a.k.a. Senpyou), an aged cat, lives at the top of the tower. He guards the Chousei water and is the keeper of the senzu seeds. Yajirobee eventually moves to the top of the tower.
The Tenkai: This is the home of Kame-sama and Mr. Popo. It is located directly above Karin Tower. Goku ends up connecting the two together with his Nyoibo. Tenkai translates to "The world in the heavens" and is large circular structure resembling the bottom half of a sphere. Kame-sama can watch events anywhere on the world from here. The Tenkai is also used as a meeting place by the Z Fighters when powerful enemies are wrecking havoc below.
Seishin to Toki no Heya: Located within the Tenkai, this translates to "room of spirit and time." It is a huge, flat, white plane as large as the Earth. The gravity is 10 times that of Earth's, while the temperature ranges from -40 to 122 F. Time flows much different within Seishin to Toki no Heya. One year inside the Room is equal to only one day outside. The Z-Fighters (or, at least the Saiyans), use this room extensively right before the Cell Game.
Using the World Setting in a game:
If running a campaign set in the Dragon Ball Z universe, the GM has a lot of leeway. Basically, he can feel free to create virtually anything he wants and not have to worry about violating any sort of established "doctrine" as to what the universe is like. Need a new alien race? Go right a head and create one.
In general, the GM should remember that the world is under a single government, but that the Earth has a lot of "wild" areas, where the law is pretty scarce. In space, Freezer seemed to be a major power, but with the destruction of the Saiyajin and Freezer himself, there is a power vacuum that could be exploited by anyone with sufficient power and troops. Toriyama himself seemed to create beings as a matter of convenience. If he needed a super-powerful entity to help/hinder Goku and company, he whipped one up out of thin air. Only Freezer seemed to exist far before he ever appeared, with Vegita mentioning him in Volume 18. As for gods, there seems to be room for "just one more." Lord Enma is more powerful than Kama-sama, while Kaio-Sama is more powerful than Enma, and, of course, Kaio-shin is more powerful than Kaio-Sama (and so on). Probably the most important point about this aspect of the Dragon Ball Z universe is that all such "divine" beings should serve a purpose. They should either be a source of powers, training, or information. Characters should not be expected to fight them, especially since so many of the gods usually outstrip our heroes in power levels when first met.
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