So your titles are passed on and you have no claim on them at all? They don't see you as their liege anymore?
Your heir gets the highest ranked title you have. If this is a duchy, he'll get that. If you have more then 1 duchy, the others are split up amonsgt your other children, and since they'll be of the same rank as your heir, they'll split. The only way to keep the realm together in a gavelkind (that I know of) is making sure your heir has a higher title (in the duchy example, a kingdom).
So, for example, lets say I have 3 sons, SonA, SonB, and SonC. Lets say I have 2 duchy titles. Upon my death, SonA will get a duchy, SonB will get a duchy, and SonC wouldn't get anything. Since SonA and SonB are the same rank now (both dukes), SonB will split to form his own duchy since he'll be like "well, we're the same rank, so I dont have to be your vassal anymore!"
Now, lets say we have the same setup, but we add a king title in there. So 2 duchy titles and 1 king title. SonA would inherit kingdom, SonB will get 1 duchy, and SonC would get 1 duchy. Since your heir is a king, SonB and SonC won't split, since you're a higher rank.
NOTE: This may ONLY work if the duchies are within the SAME DE JURE KINGDOM that the king title is for. I'm not 100% sure on that.
EDIT: MY question for you guys... when my king dies, does his gold pass to the heir, or should I try spending it all before I kick the bucket?