Models of subglacial deformable sediment and ice-free sediment transport are added to a global climate (GCM)-dynamical ice sheet model. The coupled model is applied to the evolution of early Oligocene Antarctic ice sheets, sediment distributions, and coastal sediment discharge under a range of prescribed atmospheric CO2 and orbital variations. The GCM-ice sheet model uses a computationally efficient asynchronous coupling scheme, enabling long (10 million year) integrations. The sediment component is initialized with a uniform 50m layer of regolith, assumed to have accumulated prior to the onset of widespread glaciation. Subglacial sediment deformation in the upper tens of cm is driven by basal shear stress where the basal ice is melting. The spatial distribution of sediment evolves by bulk transport of sediment under the ice, quarrying of new till by glacial ice in contact with clean bedrock, and fluvial downslope transport of freshly exposed sediment to the continental margin. With a prescribed gradual decline of atmospheric CO2 over the 10 Ma long simulations, a sudden transition occurs around 2.5 x present CO2, from relatively small land-based ice caps localized on high topography, to a single large East Antarctic ice sheet comparable to today. Much of the pre-existing sediment is transported to the coast by the action of repeated orbital cycles, funneled into continental scale drainage basins and thence to a small number of major discharge sites. The predicted spatial and temporal patterns of sediment discharge are compared with observed distributions and core records of offshore Cenozoic sedimentary deposits.