  We study the class of neutrino mass matrices with a dominant block but
unspecified O(1) coefficients, and scan the possible models by the help of
random number generators. We discuss which are the most common expectations in
dependence of the adjustable parameter of the mass matrices, "epsilon", and
emphasise an interesting sub-class of models that have large mixing angles for
atmospheric and solar neutrinos. For those models where the lepton mass
matrices are subject to Froggatt-Nielsen U(1) selection rules, we show that the
neutrino mixing matrix receives important contributions from the rotations
operating on charged lepton sector, which increase the predicted value of the
angle "theta(13)" and the ee-entry of the neutrino mass.
