Results. The angular covariance at zero separation is estimated to be 106 mu as(2), yielding a minimum (systematic) uncertainty for EDR3 parallaxes of 10.3 mu as for individual stars or compact stellar clusters. This value can be slightly reduced for globular clusters that span greater than or similar to 30 ' after considering the behavior of the angular covariance of the parallaxes for small separations. A recent parallax bias correction is found to work quite well, except perhaps for the brighter magnitudes, where improvements may be possible. The value of k is found to be 1.1-1.7 and to depend on G. We find that stars with moderately large values of the renormalized unit weight error can still provide useful parallaxes, albeit with larger values of k. We give accurate and precise Gaia EDR3 distances to the six globular clusters, and for the specific case of 47 Tuc we are able to beat the angular covariance limit through the use of the background Small Magellanic Cloud as a reference and derive a high-precision distance of 4.53 +/- 0.06 kpc. Finally, a recipe for the derivation of distances to stars and stellar clusters using Gaia EDR3 parallaxes is given.