We study germs of holomorphic distributions with "separated variables'. In codimension one, a well know example of this kind of distribution is given by the canonical contact structure on
. Another example is the Darboux distribution, which gives the normal local form of any contact structure. Given a germ
D of holomorphic distribution with separated variables in
... [Show full abstract] , we show that there exists , for some related to the Taylor coefficients of D, a holomorphic submersion such that D is completely non-integrable on each level of . Furthermore, we show that there exists a holomorphic vector field Z tangent to D, such that each level of contains a leaf of Z that is somewhere dense in the level. In particular, the field of meromorphic first integrals of Z and that of D are the same.