Let $N_{\alpha }$,B and Qβ be the weighted Nevanlinna space, the Bloch space and the Q space, respectively. Note that B and $Q_{\beta }$ are Möbius invariant, but $N_{\alpha }$ is not. We characterize, in function-theoretic terms, when the composition operator $C_{\varphi }f=f◦\varphi$ induced by an analytic self-map ϕ of the unit disk defines an operator $C_{\varphi }:N_{\alpha }\to B$, $B\to Q_{\beta }$, $N_{\alpha }\to Q_{\beta }$ which is bounded resp. compact.

We prove that a Cousin-I open set D of an irreducible projective surface X is locally Stein at every boundary point which lies in $X_{reg}$. In particular, Cousin-I proper open sets of ℙ² are Stein. We also study K-envelopes of holomorphy of K-complete spaces.