An observed warming of the Tasman Sea in recent decades has been linked to a poleward shift of the maximum wind stress curl, and a strengthening of the poleward flow along the coast of southeastern Australia. However, changes in the East Australian Current (EAC) separation latitude, as well as in the contribution of the EAC, the EAC extension and its eddy field to the total southward transport due to such a strengthening remain unknown. This study uses 30 years (1980-2010) of the Ocean Forecast for the Earth Simulator (OFES) sea surface height and velocity outputs to obtain a 3 decade long time series of i) the EAC separation latitude, ii) the southward transport along the coast of southeastern Australia (28°S-39°S), and iii) the southward transport across the EAC separation latitude. A Lagrangian approach is implemented and the spin parameter Ω is used to provide a quantitative distinction between the transports occurring outside and inside (cyclonic and anticyclonic) eddies. Significant positive trends of the low pass southward transports indicate that the intensification of the poleward flow has occurred both within the EAC and in the EAC extension. In addition, a significant increase in southward transport inside and outside eddies is found. Importantly, the contribution of eddy driven transport has a large temporal variability and shows a sharp increase from 2005 onwards. Finally our results show that the EAC has not penetrated further south but it has separated more frequently at the southernmost latitudes within the region where it typically turns eastward.