  We construct examples illustrating that dynamically-defined distributions of
holomorphic diffeomorphisms on compact complex manifolds are not necessarily
holomorphic in any open subset. More precisely, for any $n\geq 5$, we construct
a holomorphic fibered partially hyperbolic system on a complex $n$-fold, where
the center distribution is not holomorphic in any open subset. For $n=3$ we
demonstrate a contrast: the center distribution of any fibered holomorphic
partially hyperbolic diffeomorphism on a complex $3$-fold is holomorphic. In
particular, any such a system is a holomorphic skew product over a linear
automorphism on a complex $2$-torus.
