We compare the volume flux divergence of Antarctic ice shelves in 2007 and 2008 with 1979 to 2010 surface accumulation and 2003 to 2008 thinning to determine their rates of melting and mass balance. Basal melt of 1325 +/- 235 gigatons per year (Gt/year) exceeds a calving flux of 1089 +/- 139 Gt/year, making ice-shelf melting the largest ablation process in Antarctica. The giant cold-cavity Ross, Filchner, and Ronne ice shelves covering two-thirds of the total ice-shelf area account for only 15% of net melting. Half of the meltwater comes from 10 small, warm-cavity Southeast Pacific ice shelves occupying 8% of the area. A similar high melt/area ratio is found for six East Antarctic ice shelves, implying undocumented strong ocean thermal forcing on their deep grounding lines.