We investigate petrologic and physical aspects of melt extraction on the parent asteroid of the ureilite meteorites (UPB). We first develop a petrologic model for simultaneous melting and smelting (reduction of FeO by C) at various depths. For a model starting composition, determined from petrologic constraints to have been CV-like except for elevated Ca/Al (2.5 × CI), we determine (1) degree of melting, (2) the evolution of mg, (3) production of CO + CO2 gas and (4) the evolution of mineralogy in the residue as a function of temperature and pressure. We then use these relationships to examine implications of fractional vs. batch melt extraction. In the shallowest source regions (30 bars), melting and smelting begin simultaneously at 1050 °C, so that mg and the abundance of low-Ca pyroxene (initially pigeonite, ultimately pigeonite + orthopyroxene) begin to increase immediately. However, in the deepest source regions (100 bars), smelting does not begin until 1200 °C, so that mg begins to increase and low-Ca pyroxene (pigeonite) appears only after 21% melting. The final residues in these two cases, obtained just after the demise of augite, match the end-members of the ureilite mg range (94–76) in pyroxene abundance and type. In all source regions, production of CO + CO2 by smelting varies over the course of melting. The onset of smelting results in a burst of gas production and very high incremental gas/melt ratios (up to 2.5 by mass); after a few % (s)melting, however, these values drastically decline (to <0.05 in the final increments). Physical modelling based on these relationships indicates that melts would begin to migrate upwards after only 1–2% melting, and thereafter would migrate continuously (fractionally) and rapidly (reaching the surface in < a year) in a network of veins/dikes. All melts produced during the smelting stage in each source region have gas contents sufficient to cause them to erupt explosively and be lost. However, since in all but the shallowest source regions part of the melting sequence occurs without smelting, fractional melting implies that a significant fraction of UPB melts may have erupted more placidly to form a thin crust (3.3 km thick for a 100 km radius body). Our calculations suggest that melt extraction was so rapid that equilibrium trace element partitioning may not have been attained. We present a model for disequilibrium fractional melting (in which REE partitioning is limited by diffusion) on the UPB, and demonstrate that it produces a good match to the ureilite data. The disequilibrium model may also apply to trace siderophile elements, and might help explain the “overabundance” of these elements in ureilites relative to predictions from the smelting model. Our results suggest that melt extraction on the UPB was a rapid, fractional process, which can explain the preservation of a primitive oxygen isotopic signature on the UPB.