  Motivated by recent experiments, we extend the Joanny-deGennes calculation of
the elasticity of a contact line to an arbitrary contact angle and an arbitrary
plate inclination in presence of gravity. This requires a diagonalization of
the elastic modes around the non-linear equilibrium profile, which is carried
out exactly. We then make detailed predictions for the avalanche-size
distribution at quasi-static depinning: we study how the universal (i.e.
short-scale independent) rescaled size distribution and the ratio of moments of
local to global avalanches depend on the precise form of the elastic kernel.
