The Black Star is simply a re-fillable black soul gem. Black soul gems can hold any size soul from the smallest to the largest, and black soul gems are the only ones that can hold souls of playable races (humans, etc). It can still be filled with petty and common souls of mudcrabs and elk and trolls, for instance. Basically each soul gem is like a Russian nesting doll. The smallest one can only hold the smallest souls. The lesser can hold the smallest (petty) as well as lesser. The common can hold: commons, lesser, petty. Etc. The black star can hold: black souls, grand, greater, common, lesser, and petty.
Just drop it to empty (any soul gem). or the Star, just use it to recharge a weapon and it will empty.