The geomorphology of troughs crossing the Antarctic shelf is described and interpreted in terms of ice-stream hydrology. The scale of tunnel channels on the inner shelf and the absence of sediment at their mouths are taken to infer catastrophic drainage. Drumlins on the inner and outer shelves with pronounced crescentic and hairpin scours are also interpreted as products of catastrophic flow. Gullies and channels on the continental slope and turbidites on the rise and abyssal plain point to abundant meltwater discharge across the shelf. Attempts to explain this morphology and sedimentology in terms of release or discharge of meltwater by pressure melting, strain heating, Darcian flow, or advection in deforming till are shown to be unrealistic. We suggest that meltwater flow across the middle and outer shelves might have been in broad, turbulent floods, which raises the possibility that megascale glacial lineations (MSGL) on the shelf might originate by erosion in turbulent flow. This possibility is explored by use of analogs for MSGL from flood and eolian landscapes and marine environments. An extended discussion reflects on objections that stand in the way of the flood hypothesis.