1Progradational fluvio-deltaic systems tend towards but cannot reach equilibrium, a state in 2 which the longitudinal profile does not change shape and all sediment is bypassed beyond the 3 shoreline. They cannot reach equilibrium because progradation of the shoreline requires 4 aggradation along the longitudinal profile. Therefore progradation provides a negative feedback, 5 unless relative sea level falls at a sufficient rate to cause non-aggradational extension of the 6 longitudinal profile. How closely fluvio-deltaic systems approach equilibrium is dependent on their 7 progradation rate, which is controlled by water depth and downstream allogenic controls, and 8 governs sediment partitioning between the fluvial, deltaic, and marine domains. Here, six analogue 9 models of coastal fluvio-deltaic systems and small prograding shelf margins are examined to better 10 understand the effect of water depth, subsidence, and relative sea-level variations upon longitudinal 11 patterns of sediment partitioning and grain-size distribution that eventually determine large-scale 12 stratigraphic architecture. Fluvio-deltaic systems prograding in relatively deep-water environments 13 are characterized by relatively low progradation rates compared to shallow-water systems. This 14 allows these deeper water systems to approach equilibrium more closely, enabling them to 15 construct less concave and steeper longitudinal profiles that provide low accommodation to fluvial 16 systems. Glacio-eustatic sea-level variations and subsidence modulate the effects of water depth on 17 the longitudinal profile. Systems are closest to equilibrium during falling relative sea level and early 18 lowstand, resulting in efficient sediment transport towards the shoreline at those times. 19Additionally, the strength of the response to relative sea-level fall differs dependent on water depth. 20In systems prograding into deep water, relative sea-level fall causes higher sediment bypass rates 21 and generates significantly stronger erosion than in shallow-water systems, which increases the 22 probability of incised-valley formation. Water depth in the receiving basin thus forms a first-order 23 control on the sediment partitioning along the longitudinal profile of fluvio-deltaic systems and the 24 shelf clinoform style. It also forms a control on the availability of sand-grade sediment at the 25 3 shoreline that can potentially be remobilized and redistributed into deeper marine environments. 26