8The assessment and meaning of turbidite thickness statistics represent open research questions 9 for both applied and pure sedimentology. Yet thickness data collected in the field are often 10 incomplete and/or biased toward or against certain thickness classes due to bed geometry, erosion 11 and/or operational filed constraints, which largely undermine tackling such questions. However, in 12 situations where turbidity currents are ponded by basin topography so to deposit basin-wide 13 tabular beds and erosion is negligible, some of the variables of the 'bed thickness equation' can be 14 relaxed, making easier to investigate what the primary controls on turbidite thickness statistics are. 15This study reviews the bed thickness statistics of the non-channelized parts of the infill of four 16 tertiary basins of Central-Northern Apennines (Italy), where bed geometry and sedimentary 17 character have been previously assessed. Though very different in terms of size and, arguably, 18 character of feeder system and source area, these basins share a common evolution to their 19 turbidite fill with upward transition from an early ponded to a late unconfined setting of deposition. 20Based on comparison of thickness subsets from diverse locations and stratigraphic heights within 21 the basin fills of the case studies, this paper seeks to answering the following questions: i) how 22 data collection choices and field operational constraints (e.g. location, outcrop quality, use of 23 thickness from single vs. multiple correlative sections, length of the stratigraphic section from which 24 thicknesses were retrieved) can affect statistics of an empirical distribution of turbidite thicknesses? 25 ii) how depositional controls of confined vs. unconfined basins can modify the initial thicknesses 26 distribution of turbidites?; iii) is there in turbidite thickness statistics a 'flow confinement' signature 27 2 which can be used to distinguish between confined and unconfined depositional settings? Results 28 suggests that: i) best practices of data collection are crucial to a meaningful interpretation of 29 turbidite thickness data, especially in presence of stratigraphic and spatial trends of bed thickness; 30 ii) a systematic bias against cm-thick Tcd Bouma sequence turbidites deposited by small volume 31 low density flows exists, which can significantly modify the low-end tail of an empirical frequency 32 distribution of bed thickness; iii) thickness statistics of beds starting with a basal Ta/Tb Bouma 33 division bear a coherent relationship to the transition from ponded to unconfined depositional 34 settings, consisting in a reduction of variance and mean and, consequently, modification of the 35 initial thickness-frequency scaling relationship. This research highlights the role of flow stripping, 36 sediment by-pass and bed geometry in altering the initial thickness distribution of ponded turbidites 37 suggesting how, on the contrary, fully ponded mini-basins represents the ideal setting for further 38 research link...