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We show that, in quaternionic geometry, the Ward transform is a manifestationof the functoriality of the basic correspondence between the$\rho$-quaternionic manifolds and their twistor spaces. We apply this fact,together with the Penrose transform, to obtain existence results forhypercomplex manifolds and for harmonic morphisms from hyper-Kaehler manifolds.

(Pluri)harmonic morphisms and the Penrose-Ward transform