Orbits of parabolic subgroup acting on its unipotent radical

Let $P$ be a parabolic subgroup of a complex semisimple algebraic group. It is well-known that there is a dense open orbit in the unipotent radical $P_u$ of $P$ with respect to the adjoint action of $P$. This makes the problem of describing the orbital decomposition of this action rather delicate. We address this problem from the point of view of modality of action. This leads to the monotonicity results and the explicit classifications of parabolics of small modality (in particular, modality $0$, i.e., with only finitely many $P$-orbits in $P_u$).