Using a forward modeling approach based on an axisymmetric Gaussian seamount, I characterize the global seamount distribution by locating circular maxima in the gridded vertical gravity gradient field derived from altimetry collected by the Geosat and ERS-1 satellite missions. The global seamount distribution is long-tailed and resembles a power law distribution for seamounts in the height range 2--7 km. Smaller seamounts are not well isolated by my technique nor are they well resolved in the gridded data. Several factors are likely to influence the height of volcanic seamounts, such as melt availability, magma driving pressure, and plate thickness. The observed relationship between seamount gravimetric amplitudes and the age of the underlying seafloor implies that there is an upper limit on seamount heights. Whether a seamount will reach that height depends most likely on supply-side factors, such as melt availability and magma driving pressure, but the limiting height itself seems more likely to be controlled by the strength of the oceanic plate. Specifically, compressional stresses directly beneath the seamount as a consequence of the lithosphere's flexural response to loading may eventually exceed the magma driving pressure and prevent magma from reaching the surface, thus limiting the growth of the seamount. Because oceanic plate strength primarily is controlled by plate age, the limit on seamount height is inferred to be a simple function of plate age at the time of seamount emplacement. Using analytical solutions, I present a simple flexural model that predicts the observed global height-age relationship. ¿ 2001 American Geophysical Union