  This work aims to study some smoothness properties concerning the initial
value problem associated to the dispersive generalized
Benjamin-Ono-Zakharov-Kuznetsov equation. More precisely, we prove that the
solutions to this model satisfy the so-called propagation of regularity.
Roughly speaking, this principle states that if the initial data enjoys some
extra smoothness prescribed on a family of half-spaces, then the regularity is
propagated with infinite speed. In this sense, we prove that regardless of the
scale measuring the extra regularity in such hyperplane collection, then all
this regularity is also propagated by solutions of this model. Our analysis is
mainly based on the deduction of propagation formulas relating homogeneous and
non-homogeneous derivatives in certain regions of the plane.
