  Context. Gaia Early Data Release 3 (EDR3), published in December 2020,
features improved photometry and astrometry over that published in the previous
DR2 file, and includes a substantially larger number of sources, of the order
of 2,000 million, making it a paradigm of Big data Astronomy.
  Aims. We demonstrate how Gaia data mining can effectively help to solve the
issue of central star misidentification, a problem that has plagued the field
since its origin. As we did for DR2, our objective is to present a catalogue of
CSPNe with astrometric and photometric information in EDR3.
  Methods. Gaia G(BP)-G(RP) colours allow us to select the sources with
sufficient temperatures to ionize the nebula. In order to estimate the real
colour of a source, it is important to take into account interstellar
extinction and, in the case of compact nebulae, nebular extinction when
available. In addition, distances derived from EDR3 parallaxes (combined with
consistent literature values) can be used to obtain nebular intrinsic
properties from those observed. With this information, CSPNe can be plotted in
an HR diagram.
  Results. We present a catalogue of 2035 PNe with their corresponding CS
identification from among Gaia EDR3 sources. We obtain the distances for those
with known parallaxes in EDR3 (1725 PNe). In addition, for a subsample (405
PNe) with the most accurate distances, we obtain different nebular properties
such as their Galactic distribution, radius, kinematic age and morphology.
Furthermore, for a set of 74 CSPNe, we present the evolutionary state (mass and
age) derived from their luminosities and effective temperatures from
evolutionary models. Finally, we highlight the detection of several wide binary
CSPNe through an analysis of the EDR3 astrometric parameters, and we contribute
to shedding some light on the relevance of close binarity in CSPNe.
