[Abridged] Typical disc galaxies forming in a LambdaCDM cosmology encounter a violent environment, where they often experience mergers with massive satellites. The fact that disc galaxies are ubiquitous in the local Universe suggests that a quiescent history is not necessary for their formation. Modern cosmological simulations can now obtain relatively realistic populations of disc galaxies, but it still remains to be clarified how discs manage to survive massive mergers. Here we use a suite of high-resolution hydrodynamical simulations set in a LambdaCDM cosmology to elucidate the fate of discs encountering massive mergers. We extract a sample of approximately 100 disc galaxies and follow the changes in their post-merger morphologies, as tracked by their disc-to-total ratios (D/T). We also examine the relations between their present-day morphology, assembly history and gas fractions. We find that approximately half of present-day disc galaxies underwent at least one merger with a satellite of total mass exceeding the host systems stellar mass, a third had mergers with satellites of mass exceeding 3 times the hosts stellar mass, and approximately one-sixth had mergers with satellites of mass exceeding 10 times of the hosts stellar mass. These mergers lead to a sharp, but often temporary, decrease in the D/T of the hosts, implying that discs are usually disrupted but then quickly re-grow. To do so, high cold gas fractions are required post-merger, as well as a relatively quiescent recent history (over a few Gyrs before z=0). Our results show that discs can form via diverse merger pathways and that quiescent histories are not the dominant mode of disc formation.
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