The unbalance of set systems

The unbalance of an intersecting family F is defined as |F| - d(F), where d(F) is the maximum degree of F i.e. the maximum of |{F epsilon F : x epsilon F}| over all vertices x. We show that the unbalance of a k-uniform intersecting family is at most [GRAPHICS] when n >= 6k(3) and we determine all families achieving this bound.