  Context. Planetary nebulae (PNe) are a brief but important phase of stellar
evolution. The study of Galactic PNe has historically been hampered by
uncertain distances, but the parallaxes of PN central stars (CSPNe) measured by
Gaia are improving the situation. Aims. Gaia's Early Data Release 3 (EDR3)
offers higher astrometric precision and greater completeness compared to
previous releases. Taking advantage of these improvements requires that the
CSPNe in the catalogue be accurately identified. Methods. We applied our
automated technique based on the likelihood ratio method to cross match known
PNe with sources in Gaia EDR3, using an empirically derived position and colour
distribution to score candidate matches. Results. We present a catalogue of
over 2000 sources in Gaia EDR3 that our method has identified as likely CSPNe
or compact nebula detections. We show how the more precise parallaxes of these
sources compare to previous PN statistical distances and introduce an approach
to combining them to produce tighter distance constraints. We also discuss
Gaia's handling of close companions and bright nebulae. Conclusions. Gaia is
unlocking new avenues for the study of PNe. The catalogue presented here will
remain valid for the upcoming Gaia Data Release 3 (DR3) and thus provide a
valuable resource for years to come.
