Disjoint unions of complete minors

Given integers r and s, and n large compared to r and s, we determine the maximum size of a graph of order n   having no minor isomorphic to sKrsKr, the union of s   disjoint copies of KrKr.The extremal function depends on the relative sizes of r and s. If s is small compared to r the extremal function is essentially independent of s. On the other hand, if s is large compared to r  , there is a unique extremal graph Ks(r-1)-1+K¯n-s(r-1)+1; this assertion is a generalization of the case r=3r=3 which is a classical result of Erdős and Pósa.