Disjoint complete minors and bipartite minors

Let rr, ss and tt be integers and let c(r)c(r) be such that every graph GG with at least c(r)|G|c(r)|G| edges has a KrKr minor. We prove that there is a function fr,s,t(n)fr,s,t(n), with fr,s,t(n)=o(n)fr,s,t(n)=o(n) as n→∞n→∞, such that every graph of order nn and having at least (c(r)+s−1)n+fr,s,t(n)(c(r)+s−1)n+fr,s,t(n) edges contains either tt disjoint KrKr minors or a Ks,tKs,t minor.