The God of Death is given primary charge over Death and the Underworld. He is rather lazy as gods go, being content to send his servants to handle death on his behalf. He enjoys competition, and thus is willing to gamble the spirits in his Underworld for a chance at a good contest, since he gets precious little entertainment. He spends most of his time partaking in these contests or occasionally doing some of his work himself where he has a personal interest in it. He also has a tendency to open large chasms underneath things when he gets angry, causing parts of the surface to fall into the Underworld (though this is rather rare).
Just like many of the other gods, Death has a Champion, his primary mortal representative. The Champion of Death is Immortal and impossible to kill by mundane means. Currently has stitch marks around his neck where he had sewn his head back on after the champion of War cut it off to see if he really was immortal. If his body is destroyed beyond repair, he can ask the god of Death to fashion him a new one, which he invariably will. Can also contact the spirits of the underworld and communicate with the dead, but cannot directly summon them or anything.
However, the God of Death is almost unique in having an additional servant, the horseman of Death. He is death's most trusted and powerful servant, wielding a wickedly curved scythe and a razor sharp sword. He sometimes handles spirits who wish to challenge Death to combat of any sort. It is said that should any mortal manage to kill the horseman in honourable combat, that mortal would then take his place.
While the Underworld is far too large for the god of Death to entirely control, he does have control over his contest hall and surrounding parts of the Underworld. In his hall, Death makes the rules, basically. Though the Overgod of course has veto on this since he granted Death this boon. The area above the contest hall on the surface also falls under Death's jurisdiction, and is the only place the spirits of the deceased are allowed to make any sort of contact with the surface, and even then only via Death's champion. The champion, naturally, lives in the area.
(Note - this article is mostly in disarray, so will people please arrange it so it looks better and such? =P)