When I mouse over certain Muslim provinces, it shows ("Name, Castille") in the popup.
I'm playing Castille, just started a new game.
What does this indicate? Do I have some kind of claim to that province?
That province's natural liege is the Kingdom of Castile. Independant Counts and Dukes with titles in that area will eventually pledge allegiance to the King of Castile. But only if the religion matches -- a Catholic Duke is not likely to voluntarily pledge allegiance to an Orthodox King.
If Kingdom of Castile does not exist, and Christian controls 2/3 of the provinces of Castile, he can create the Kingdom of Castile. If he was already a King he gets another King-title, and slightly more prestige each month. If he was a Duke or Count he gets promoted, becomes independant, and has to do a save/reload. In either case he gains no new provinces, but eventually all Dukes and Counts with capitals in Castile will pledge allegiance to him.
If the Kingdom of castile does exist, and a Christian controls 2/3 of it's provinces, the Christian can get a very cheap claim on the title by usurping it. He can do this even if he doesn't have enough prestige to pay for the claim -- his prestige will go negative. Usurping is also nice because it does not give BB.
Nick