We study the dynamics of melting in the Hawaiian plume using a 3D variable-viscosity convection model outfitted with a melting parameterization that permits calculation of the local melting rate and the distribution of buoyant depleted residual material. From a suite of 45 steady-state numerical experiments, we derive complete scaling laws for the total rate of melting M and the height H and width W of the topographic swell as functions of the lithospheric thickness zl and the plume's maximum potential temperature θi, thermal buoyancy flux B, and minimum viscosity ηp. Assuming 1500°C<θi<1600°C, the observed values of M, H and W can only be matched if zl≤89 km, 2200 kg s−1 ≤B≤3500 kg s−1, and ηp≥5×1017 Pa s. We study a reference Hawaiian model satisfying these constraints. The depletion anomaly is narrower than the thermal anomaly, and carries 24% of the total (thermal plus depletion) buoyancy flux. Its buoyancy contributes 350 m of the uplift along the swell axis, and reduces the geoid/topography ratio by 16% relative to a model without depletion buoyancy. All the material that melts comes from the hottest central part of the plume, and no direct melting of the asthenosphere or lithosphere occurs. Melting occurs both in a primary melting zone above the plume stem and in a weaker secondary melting zone 300–500 km downstream, separated by an interval where no melting occurs. We propose that the preshield-, shield-, and postshield stages of Hawaiian volcanism are generated by the primary melting zone, and the rejuvenated stage by the secondary melting zone.