  We study the splitting behaviour of quasilinear $p$-forms in the spirit of
the theory of nondegenerate quadratic forms over fields of characteristic
different from 2 using an analogue of M. Knebusch's generic splitting tower.
Several new applications to the theory of quasilinear quadratic forms are
given. Among them, we can mention an algebraic analogue of A. Vishik's theorem
on "outer excellent connections" in the motives of quadrics, partial results
towards a quasilinear analogue of N. Karpenko's theorem on the possible values
of the invariant $i_1$, and a proof of a conjecture of D. Hoffmann on quadratic
forms with maximal splitting in the quasilinear case.
