The thermal radio emission of novae during outburst enables us to derive fundamental quantities such as the ejected mass, kinetic energy, and density profile of the ejecta. Recent observations with newly-upgraded facilities such as the VLA and e-MERLIN are just beginning to reveal the incredibly complex processes of mass ejection in novae (ejections appear to often proceed in multiple phases and over prolonged timescales). Symbiotic stars can also exhibit outbursts, which are sometimes accompanied by the expulsion of material in jets. However, unlike novae, the long-term thermal radio emission of symbiotics originates in the wind of the giant secondary star, which is irradiated by the hot white dwarf. The effect of the white dwarf on the giant's wind is strongly time variable, and the physical mechanism driving these variations remains a mystery (possibilities include accretion instabilities and time-variable nuclear burning on the white dwarf's surface). The exquisite sensitivity of SKA1 will enable us to survey novae throughout the Galaxy, unveiling statistically complete populations. With SKA2 it will be possible to carry out similar studies in the Magellanic Clouds. This will enable high-quality tests of the theory behind accretion and mass loss from accreting white dwarfs, with significant implications for determining their possible role as Type Ia supernova progenitors. Observations with SKA1-MID in particular, over a broad range of frequencies, but with emphasis on the higher frequencies, will provide an unparalleled view of the physical processes driving mass ejection and resulting in the diversity of novae, whilst also determining the accretion processes and rates in symbiotic stars. ; Comment: 13 pages, 3 figures, in proceedings of "Advancing Astrophysics with the Square Kilometre Array", PoS(AASKA14)116, in press