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Coastal polynyas are key formation regions for dense shelf water (DSW) that ultimately contributes to the ventilation of the ocean abyss. However, not all polynyas form DSW. We examine how the physiographic setting, water‐mass distribution and transformation, water column stratification, and sea‐ice production regulate DSW formation in four East Antarctic coastal polynyas. We use a salt budget to estimate the relative contribution of sea‐ice production and lateral advection to the monthly change in salinity in each polynya. DSW forms in Mackenzie polynya due to a combination of physical features (shallow water depth and a broad continental shelf) and high sea‐ice production. Sea‐ice formation begins early (March) in Mackenzie polynya, counteracting fresh advection and establishing a salty mixed layer in autumn that preconditions the water column for deep convection in winter. Sea‐ice production is moderate in the other three polynyas, but saline DSW is not formed (a fresh variety is formed in the Barrier polynya). In the Shackleton polynya, brine rejection during winter is insufficient to overcome the very fresh autumn mixed layer. In Vincennes Bay, a strong inflow of modified Circumpolar Deep Water stratifies the water column, hindering deep convection and DSW formation. Our study highlights that DSW formation in a given polynya depends on a complex combination of factors, some of which may be strongly altered under a changing climate, with potentially important consequences for the ventilation of the deep ocean, the global meridional overturning circulation, and the transport of ocean heat to Antarctic ice shelves. Plain Language Summary: Coastal polynyas are regions of open water surrounded by sea ice. As sea ice forms, it is pushed offshore by strong winds blowing from the Antarctic continent, keeping the polynya ice‐free. Salt is released into the water below as sea ice forms, increasing the salinity and density of the water column. In some polynyas, this water is dense enough to sink from the continental shelf to supply a network of bottom ocean currents that influences global climate. In other polynyas, the water in winter never gets dense enough to reach the ocean abyss. Using data collected by instrumented elephant seals, we investigated the main factors controlling dense water formation in four East Antarctic polynyas. We found that dense water production is related to the strength of sea‐ice formation, as expected, but also depends on the salinity at the start of winter. The geographical and physical characteristics of the polynyas and regional circulation also modulate the final water density. Our findings provide insight into how dense water formation in East Antarctic polynyas might respond to future changes in climate and thereby influence the transport of ocean heat to the Antarctic continent and the melt of ice shelves. Key Points: We determined the physical factors enhancing (or hindering) dense shelf water (DSW) formation in four East Antarctic polynyas during a well sampled yearRelatively high salinity in early winter and high sea‐ice formation favor DSW formation in Mackenzie PolynyaThe properties and volume of DSW formed in a coastal polynya depend on its preconditioning as well as on sea‐ice formation [ABSTRACT FROM AUTHOR]

• We quantified dense shelf water formation from sea ice freezing in the Gulf of Anadyr. • Sea ice freezing alters the relationships between salinity and oxygen isotopic ratio. • Dense shelf water formed in the Gulf of Anadyr even in a year of low ice production. We analyzed temperature and salinity data and oxygen isotope ratios (δ18O) in summer 2018 in order to quantify the formation of dense shelf water (DSW) associated with sea ice freezing in the Gulf of Anadyr in the northwestern Bering Sea. Salinity and δ18O displayed a strong linear relationship in samples upstream (southwest) of the Gulf of Anadyr. However, in bottom water (>26.5 σ θ) in the northern Gulf of Anadyr, where a large polynya is the site of high sea ice production in winter, salinity was clearly higher than in the upstream water, whereas δ18O was in the same range. This deviation is consistent with the formation of sea ice through brine rejection and subsequent DSW formation, causing an increase of salinity without changing δ18O. A mass balance calculation based on these results yielded an estimated production of sea ice equivalent to a thickness 0.7 m, a result that matched an independent estimate of 2018 annual ice production based on satellite data. Even though the winter of 2018 had a historically low sea ice extent in the Bering Sea, including the Gulf of Anadyr, our results indicate continued DSW formation in the Gulf of Anadyr. [ABSTRACT FROM AUTHOR]