Bounded quantifier depth spectra for random graphs

For which αα there are first order graph statements AA of given quantifier depth kk such that a Zero–One law does not hold for the random graph G(n,p(n))G(n,p(n)) with p(n)p(n) at or near (there are two notions) n−αn−α? A fairly complete description is given in both the near dense (αα near zero) and near linear (αα near one) cases.