Let $RRat_k$ ($CP^n$) denote the space of basepoint-preserving conjugation-equivariant holomorphic maps of degree k from $S^2$ to $CP^n$. A map f ; $S^2 { o}CP^n$ is said to be full if its image does not lie in any proper projective subspace of $CP^n$. Let $RF_k(CP^n)$ denote the subspace of $RRat_k(CP^n)$ consisting offull maps. In this paper we determine $H{ast}(RF_k(CP^2); Z/p)$ for all primes p.