  We present results from the first population synthesis study of protostellar
discs. We analyse the evolution and properties of a large sample of
protostellar discs formed in a radiation hydrodynamical simulation of star
cluster formation. Due to the chaotic nature of the star formation process, we
find an enormous diversity of young protostellar discs, including misaligned
discs, and discs whose orientations vary with time. Star-disc interactions
truncate discs and produce multiple systems. Discs may be destroyed in
dynamical encounters and/or through ram-pressure stripping, but reform by later
gas accretion. We quantify the distributions of disc mass and radii for
protostellar ages up to $\approx 10^5$ yrs. For low-mass protostars, disc
masses tend to increase with both age and protostellar mass. Disc radii range
from of order ten to a few hundred au, grow in size on timescales $\le 10^4$
yr, and are smaller around lower-mass protostars. The radial surface density
profiles of isolated protostellar discs are flatter than the minimum mass solar
nebula model, typically scaling as $\Sigma \propto r^{-1}$. Disc to protostar
mass ratios rarely exceed two, with a typical range of $M_{\rm d}/M_* = 0.1-1$
to ages $\le 10^4$ yrs and decreasing thereafter. We quantify the relative
orientation angles of circumstellar discs and the orbit of bound pairs of
protostars, finding a preference for alignment that strengths with decreasing
separation. We also investigate how the orientations of the outer parts of
discs differ from the protostellar and inner disc spins for isolated protostars
and pairs.
