  We study the characteristics of galaxy protoclusters using the latest
L-galaxies semi-analytic model. Searching for protoclusters on a scale of $\sim
10 \, \mathrm{cMpc}$ gives an excellent compromise between the completeness and
purity of their galaxy populations, leads to high distinction from the field in
overdensity space, and allows accurate determination of the descendant cluster
mass. This scale is valid over a range of redshifts and selection criteria. We
present a procedure for estimating, given a measured galaxy overdensity, the
protocluster probability and its descendant cluster mass for a range of
modelling assumptions, particularly taking into account the shape of the
measurement aperture. This procedure produces lower protocluster probabilities
compared to previous estimates using fixed size apertures. The relationship
between AGN and protoclusters is also investigated, and shows significant
evolution with redshift; at $z \sim 2$ the fraction of protoclusters traced by
AGN is high, but the fraction of all AGN in protoclusters is low, whereas at $z
\geqslant 5$ the fraction of protoclusters containing AGN is low, but most AGN
are in protoclusters. We also find indirect evidence for the emergence of a
passive sequence in protoclusters at $z \sim 2$, and note that a significant
fraction of all galaxies reside in protoclusters at $z \geqslant 2$,
particularly the most massive.
