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We display four approximation theorems for manifold-valued mappings. Thefirst one approximates holomorphic embeddings on pseudoconvex domains in $\BbbC^n$ with holomorphic embeddings with dense images. The second theoremapproximates holomorphic mappings on complex manifolds with bounded images withholomorphic mappings with dense images. The last two theorems work the otherway around, constructing (in different settings) sequences of holomorphicmappings (embeddings in the first one) converging to a mapping with dense imagedefined on a given compact minus certain points (thus in general notholomorphic).

Approximation and accumulation results of holomorphic mappings with dense image