Not yet reviewed by Pith; the record is open.

CONTEXT. Gaia EDR3 has produced parallaxes for 1.468x10^9 sources but there are calibration issues that require corrections to the published values and uncertainties. AIMS. We want to characterize the behavior of the uncertainties of the Gaia EDR3 parallaxes. We also aim to provide a procedure for the calculation of distances to stars and stellar clusters. METHODS. We reanalyze some of the data in the calibration papers for QSO and LMC parallaxes and combine those results with measurements for six bright GCs. We calculate the angular covariance of EDR3 parallaxes at small separations based on the LMC results and combine it with the results for larger angles using QSOs to obtain an analytical formula for the angular covariance over the whole sky. The results for the six GCs are used to validate the parallax bias correction as a function of magnitude, color, and ecliptic latitude and to determine the constant used to convert internal uncertainties to external ones. RESULTS. The angular covariance at zero separation is 106.2 muas^2, yielding a minimum uncertainty for EDR3 parallaxes of 10.3 muas for individual stars. That value can be only slightly reduced for GCs after considering the behavior of the angular covariance of the parallaxes for small separations. The Lindegren et al. parallax bias correction works quite well, except for the brighter magnitudes, suggesting improvements may be possible there. The value of k is 1.1-1.7 and depends on G. Stars with moderately large values of RUWE can still provide useful parallaxes albeit with larger values of k. We give accurate and precise Gaia EDR3 distances to the six GCs and for the specific case of 47 Tuc we are able to beat the angular covariance limit 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. [ABRIDGED]