  An asymptotic description of the formation of dispersive shock waves in
solutions to the generalized Kadomtsev--Petviashvili (KP) equation is
conjectured. The asymptotic description based on a multiscales expansion is
given in terms of a special solution to an ordinary differential equation of
the Painleve' I hierarchy. Several examples are discussed numerically to
provide strong evidence for the validity of the conjecture.
