  In this paper, we prove three related results;
  (1) Extension of our result in [10] to all generic hypersurfaces. More
precisely, the normal sheaf of a generic rational map $c_0$ to a generic
hypersurface $X_0$ of $\mathbf P^n, n\geq 4$ has a vanishing higher cohomology,
\begin{equation} H^1(N_{c_0/X_0})=0. \end{equation}
  As applications we give
  (2) A solution to a Voisin's conjecture [9] on a covering of a generic
hypersurface by rational curves
  (3) A classification of rational curves on hypersurfaces of general type--a
solution to another Voisin's conjecture [9].
