We present a large parameter study where we investigate the structure of white dwarf (WD) merger remnants after the dynamical phase. A wide range of WD masses and compositions are explored and we also probe the effect of different initial conditions. We investigated the degree of mixing between the WDs, the conditions for detonations as well as the amount of gas ejected. We find that systems with lower mass ratios have more total angular momentum and as a result more mass is flung out in a tidal tail. Nuclear burning can affect the amount of mass ejected. Many WD binaries that contain a helium-rich WD achieve the conditions to trigger a detonation. In contrast, for carbon-oxygen transferring systems only the most massive mergers with a total mass above ~2.1 solar masses detonate. Even systems with lower mass may detonate long after the merger if the remnant remains above the Chandrasekhar mass and carbon is ignited at the centre. Finally, our findings are discussed in the context of several possible observed astrophysical events and stellar systems, such as hot subdwarfs, R Coronae Borealis stars, single massive white dwarfs, supernovae of type Ia and other transient events. A large database containing 225 white dwarf merger remnants is made available via a dedicated web page.
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