To be more precise (spoilers for Psycho Busters I guess):
Perfect World gives Kakeru (well, actually the Chrono Diver using it, but that category consists entirely of Kakeru and his clone) editorial mandate on space/time in a zone around him after he activates Perfect World. It started at ten meters, but his clone managed to isolate an entire city in space/time and Kakeru basically curbstomped him with his eyes closed in their last fight so his range is probably at least city-sized by the end.
It's actually explicitely not time control, but it has the same ultimate effect. It freezes everything in place and also allows Kakeru to pause or rewind individual timelines (for example, he rewinds a corpse to bring them back to life) and do esoteric stuff like punch at a point in time, freeze the kinetic impact, rewind the rest and repeat so that he punches the other guy a lot simultaneously. He can also freely move stuff around while time is stopped - in the previous example, he was actually punching the wall but when he got to the end of the loop he moved himself and the kinetic energy to the other guy's right to hit him instead.
Another thing, which is what makes it really hilarious, is that Perfect World is automatically activated when Kakeru dies, rewinds time to the point before he died and then lets him edit. Before he knew he had powers, this manifested as a series of very unbelievable coincidences saving him (Throwing a pencil at him with your telekinesis? A piece of concrete falls from the ceiling at the exact time to intercept it!)
After he got conscious control over it, he could actually change things in that mode. (Presented as him standing outside of time and space and looking in at the scene of himself getting killed.)
Oddly, people who are getting screwed over by Perfect World (say, killing Kakeru but being punched by him instead.) keep a sense of Déja Vu, where they're convinced that they hit him except they didn't and got punched.
The one downside is that Perfect World really fucks with the space/time continuum due to modifying the individual timelines of stuff and eventually collapses the whole thing.