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Almost all heat reaching the bases of Antarctica's ice shelves originates from warm Circumpolar Deep Water in the open Southern Ocean. This study quantifies the roles of mean and transient flows in transporting heat across almost the entire Antarctic continental slope and shelf using an ocean/sea ice model run at eddy- and tide-resolving (1/48°) horizontal resolution. Heat transfer by transient flows is approximately attributed to eddies and tides via a decomposition into time scales shorter than and longer than 1 day, respectively. It is shown that eddies transfer heat across the continental slope (ocean depths greater than 1,500 m), but tides produce a stronger shoreward heat flux across the shelf break (ocean depths between 500 m and 1,000 m). However, the tidal heat fluxes are approximately compensated by mean flows, leaving the eddy heat flux to balance the net shoreward heat transport. The eddy-driven cross-slope overturning circulation is too weak to account for the eddy heat flux. This suggests that isopycnal eddy stirring is the principal mechanism of shoreward heat transport around Antarctica, though likely modulated by tides and surface forcing.