What Dragonball Series is this?

hmmm...well I know that they are creating Dragonball Kai, which I had read was a remastered version of Dragonball Z, in which the animation is remastered and it is changed slightly to match more closely with the manga, as well as move the plot along more quickly. This is what I ume you mean, but I don't know if Dragonball Kai extends to both the Dragonball Z AND Dragonball franchises.