Since Kim-Jong un is in a vegetable state (he's sick) (roomers say he's dead but he's not!) who would take his place if he were to die? ...

His sister clearly states that she would take over if he were to die!

And usually it's the family members that would take over anyways

The most likely outcome is that Kim's sister, Kim Yo Jong, would take over.

Explanation:

The state deifies the Kims, and no other family member is as well positioned. Kim already had his half brother and his uncle killed. Kim has an older brother, Kim Jong Chul, but he was already passed over for the leadership by his father because, like Fredo Corleone, he was considered too weak. Finally there is Kim Jong Un's uncle Kim Pyong Il who served as a diplomat abroad for 40 years and only recently returned to Pyongyang. He is more likely to be an adviser to Kim Yo Jong than ruler himself.