I don't think "leak" is the right way to think about it. There's are birthday bounds on the transform and, for nonce-based modes, on the nonces used for successive encryptions. I'm not sure it's really meaningful to think about the incremental marginal degree of "leakage" with each successive ciphertext up to that limit. We're coming up to the limit of what I'm comfortable talking about though; this is normally the point where 'pbsd jumps in to explain why what I'm saying is dumb.