  We introduce and compute the class of a number of effective divisors on the
moduli space of stable maps $\bar M_{0,0}(P^{r},d)$, which, for small d,
provide a good understanding of the extremal rays and the stable base locus
decomposition for the effective cone. We also discuss various birational models
that arise in Mori's program, including the Hilbert scheme, the Chow variety,
the space of $k$-stable maps, the space of branchcurves and the space of
semi-stable sheaves.
