We present a technique which uses the large set of expendable bathythermograph data that are available in the waters off Eastern Australia to correct sampling errors in the mass transport function calculated from the much more limited number of deep hydrology stations. This technique utilizes the close correlation between temperature at a single depth and subsurface steric height, found in these waters, to perform the correction. After corrections are applied, it is found that a mass transport function for the top 2000 dbar can be used to estimate the net geostrophic outflows from the Tasman and Coral seas; it balances Ekman inflows to within −0.4±2.0 Sv (1 Sv = 1.0×106 m3 s−1). The mass transport closure allows a much improved determination of the distribution of individual transport components into the region to be obtained, including a robust estimate of the net southward transport through the whole width of the Tasman Sea (including the East Australian Current (EAC)) of 9.4 Sv, through a section at 28°S between the coast and 171°E. A more direct determination of this Tasman Sea transport, which uses annual mean alongshore currents on the shelf to infer mass transport on the slope, provides an independent confirmation. Mass budgets between density surfaces are also examined; for the deeper layers we find a closure of the mass budget within 10% of the net inflow (a maximum misclosure of 0.9 Sv), suggesting little diapycnal mixing. The geostrophic inflow upwells as it flows south in the EAC at a rate of about 3 Sv at a 250 m depth. The net transport balance along the path also allows the first determination of the heat transport associated with the mean mass transport into the Tasman and Coral seas to be obtained (we have not considered any contributions from eddy heat transport). There is a small net inflow of heat transport to the region of 0.13×1015 W, with more heat entering the Tasman Sea than the Coral Sea. The net upward heat flux of 24 W m−2 (heat loss to the atmosphere) is consistent with values given in climatologies obtained from direct surface flux calculations. The results from a Sverdrup‐Munk model agree broadly with the the observed pattern of the mass transport function, particularly the location of the boundary currents, although the model transports are generally higher.