The northern Flinders Ranges and eastern Willouran Ranges, South Australia, expose Neoproterozoic salt diapirs, salt sheets, and associated growth strata that provide a natural laboratory for testing and refining models of allochthonous salt initiation and emplacement. The diapiric Callanna Group (similar to 850-800 Ma) comprises a lithologically diverse assemblage of brecciated rocks that were originally interbedded with evaporites that are now absent. Using stereonet analysis to derive three-dimensional information from two-dimensional outcrops of stratal geometries flanking salt diapirs and beneath salt sheets, we evaluate 10 examples of the transition from steep diapirs to salt sheets, 3 of ramp-to-flat geometries, and 2 of flat-to-ramp transitions. Stratal geometries adjacent to feeder diapirs range from a minibasin-scale megaflap to halokinetic drape folds to high-angle truncations and appear to have no relationship to subsequent allochthonous salt development. In all cases, the transition from steep diapirs to salt sheets is abrupt and involved piston-like breakthrough of thin roof strata, which permitted salt to flow laterally. We suggest two models to explain the transition from steep diapirs to subhorizontal salt: (1) salt-top breakout, where salt rise occurs inboard of the salt flank, thereby preserving part of the roof strata beneath the sheet; and (2) salt-edge breakout, where rise occurs at the edge of the diapir with no roof preservation. Lateral emplacement of salt sheets is dependent on the interplay between the rate of salt supply to the front of the sheet and the sediment-accumulation rate. When the ratio of salt-supply rate to sediment-accumulation rate is high to moderate, thrust advance produces base-salt flats and truncation ramps, respectively. Halokinetic folds are absent because the thrust emerges at the base of the sea-floor scarp and mass-transport complexes are rare as a result of relatively low scarp relief. If the ratio is low, pinned inflation leads to drape folding of the top salt and cover into a fold ramp, with occasional slumping of the sheet and its roof and further breakout on thrust or reverse faults. In the shallow-water depositional environments of South Australia, lateral emplacement of salt sheets occurred through some combination of thrust advance, extrusive advance, and open-toed advance, with no evidence for subsalt thrust imbricates, shear zones, or continuous rubble zones. In deep-water environments, such as the northern Gulf of Mexico, thrust imbricates and rubble zones, which represent slumped carapace, are more common. The presence of slumped carapace is caused primarily by higher topographic relief related to thicker hemipelagic roofs, a lack of dissolution, and gravity-driven transport of overburden strata to the toes of large canopies.