We construct one-dimensional steady-state models of accretion discs produced by the tidal disruption of a white dwarf (WD) by a neutron star (NS) or stellar mass black hole (BH). At radii r ≲ 108.5–109 cm the mid-plane density and temperature are sufficiently high to burn the initial WD material into increasingly heavier elements (e.g. Mg, Si, S, Ca, Fe and Ni) at sequentially smaller radii. When the energy released by nuclear reactions is comparable to that released gravitationally, we term the disc a nuclear-dominated accretion flow (NuDAF). At small radii ≲107 cm iron photodisintegrates into helium and then free nuclei, and in the very innermost disc cooling by neutrinos may be efficient. At the high accretion rates of relevance ∼10−4 to 0.1 M⊙ s−1, most of the disc is radiatively inefficient and prone to outflows powered by viscous dissipation and nuclear burning. Outflow properties are calculated by requiring that material in the mid-plane be marginally bound (Bernoulli constant ≲ 0), due (in part) to cooling by matter escaping the disc. For reasonable assumptions regarding the properties of disc winds, we show that a significant fraction (≳ 50–80 per cent) of the total WD mass is unbound. The composition of the ejecta is predominantly O, C, Si, Mg, Ne, Fe and S [He, C, Si, S, Ar and Fe], in the case of C–O [pure He] WDs, respectively, along with a small quantity ∼10−3 to 10−2 M⊙ of radioactive 56Ni and, potentially, a trace amount of hydrogen. Depending on the pressure dependence of wind cooling, we find that the disc may be thermally unstable to nuclear burning, the likelihood of which increases for higher mass WDs. We use our results to evaluate possible electromagnetic counterparts of WD–NS/BH mergers, including optical transients powered by the radioactive decay of 56Ni and radio transients powered by the interaction of the ejecta with the interstellar medium. We address whether recently discovered subluminous Type I supernovae result from WD–NS/BH mergers. Ultimately assessing the fate of these events requires global simulations of the disc evolution, which capture the complex interplay between nuclear burning, convection and outflows.