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Diplomatic annexation is effectively the same as military annexation-their lands become yours.

They must have been your vassals for at least ten years, have a relation to you of +190 or greater, have a common border with you and be in your military alliance. Before the Edict of Toleration they must be of the same religion as you (I believe, someone is sure to jump in if I'm wrong.) If they accept you get 1 BB point for each province of the annexed nation, but you don't get the automatic 5BB hit of a military annexation. Nationalism still rears its ugly head for thirty years, but that's no sweat.:)