  [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 system's stellar mass, a
third had mergers with satellites of mass exceeding 3 times the host's stellar
mass, and approximately one-sixth had mergers with satellites of mass exceeding
10 times of the host's 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.
