How does a black hole horizon start?

When a black hole is created by gravitational collapse, there is a region of spacetime before the collapse where there is no horizon. Before the matter can fall through the horizon and create a black hole, the horizon has to start and expand to meet the matter. The starting point or points is where the generators enter the horizon. This set is a lower-dimensional, connected subset of a spacelike surface. By way of examples we will discuss the early configuration of the horizon to the time that matter enters.