The saturation function of complete partite graphs

A graph G is called F-saturated if it is F-free but the addition of any missing edge to G creates a copy of F. Let the saturation function sat(n, F) be the minimum number of edges that an F-saturated graph on n vertices can have. We determine this function asymptotically for every fixed complete partite graph F as n tends to infinity and give some structural information about almost extremal F-saturated graphs. If the two largest parts of F have different sizes, then we can reduce the error term to an additive constant.