  Based on existing data, we argue for a peculiar structure of the neutrino
mass matrix, that has a block of relatively large elements--a dominant block.
We analyze this ansatz and extract its predictions, assuming that the O(1)
coefficients (that are needed to define the model fully) are random variables.
Further insights are obtained by postulating that this structure of the mass
matrix is due to U(1) selection rules, a la Froggatt and Nielsen. A
particularly interesting case emerges, when the angle theta(13) (namely, the
mixing U(e3)) is within reach for next generation experiments, and the large
mixing angle solution for solar neutrinos is the preferred one.
