Analytic sets and extension of holomorphic maps of positive codimension

Let D, (D') be arbitrary domains in ({mathbb C}^n) and ({mathbb C}^N) respectively, (1, both possibly unbounded and (M subseteq partial D), (M'subseteq partial D') be open pieces of the boundaries. Suppose that (partial D) is smooth real-analytic and minimal in an open neighborhood of ({bar{M}}) and (partial D') is smooth real-algebraic and minimal in an open neighborhood of ({bar{M}'}). Let (f: Drightarrow D') be a holomorphic mapping such that the cluster set (mathrm{cl}_{f}(M)) does not intersect (D'). It is proved that if the cluster set (mathrm{cl}_{f}(p)) of some point (pin M) contains some point (qin M') and the graph of f extends as an analytic set to a neighborhood of ((p, q)in {mathbb {C}}^n times {mathbb C}^N), then f extends as a holomorphic map to a dense subset of some neighborhood of p. If in addition, (M =partial D), (M'=partial D') and (M') is compact, then f extends holomorphically across an open dense subset of (partial D).