We detail the stratigraphic variability of turbidite thickness statistics of four tertiary basins of Central and northern Apennine which share a common stratigraphic evolution from an early ponded to a late unconfined depositional setting.

We carry out an assessment of likely sampling biases linked to location and thickness of the studied unit which likely affect turbidite thickness statistics in presence of stratigraphic and spatial trends.

We document a systematic bias against thin beds which can lead to a significant modification of the actual turbidite thickness frequency distribution.

We show how thickness statistics of the deposit of large flows are modified due to transition from a ponded to a partially ponded and an unconfined depositional setting.

We highlight the role of flow stripping, sediment by-pass and bias against thin beds in modifying the initial frequency distribution of turbidite thickness of an initially ponded basin as a result of enlargement of the host basin and lowering of the height of the enclosing topography associated to basin infilling.

We test the applicability of the our findings to assessment of ponding from open-hole logs of a single well in a ‘fill to spill’ turbidite minibasin.