Maximal and minimal height distributions of fluctuating interfaces

We study numerically the maximal and minimal height distributions (MAHD, MIHD) of the nonlinear interface growth equations of second and fourth order and of related lattice models in two dimensions. MAHD and MIHD are different due to the asymmetry of the local height distribution, so that, in each class, the sign of the relevant nonlinear term determines which one of two universal curves is the MAHD and the MIHD. The average maximal and minimal heights scale as the average roughness, in contrast to Edwards-Wilkinson (EW) growth. All extreme height distributions, including the EW ones, have tails that cannot be fit by generalized Gumbel distributions.