  Locally, a screen integrable globally null manifold $M$ splits through a
Riemannian leaf $M'$ of its screen distribution and a null curve $\mathcal{C}$
tangent to its radical distribution. The leaf $M'$ carries a lot of geometric
information about $M$ and, in fact, forms a basis for the study of expanding
and non-expanding horizons in black hole theory. In the present paper, we
introduce a degenerate Ricci-type flow in $M'$ via the intrinsic Ricci tensor
of $M$. Several new gradient estimates regarding the flow are proved.
