We have estimated global air-sea CO2 fluxes (fgCO(2)) from the open ocean to coastal seas. Fluxes and associated uncertainty are computed from an ensemble-based reconstruction of CO2 sea surface partial pressure (pCO(2)) maps trained with gridded data from the Surface Ocean CO2 Atlas v2020 database. The ensemble mean (which is the best estimate provided by the approach) fits independent data well, and a broad agreement between the spatial distribution of model-data differences and the ensemble standard deviation (which is our model uncertainty estimate) is seen. Ensemble-based uncertainty estimates are denoted by +/- 1 sigma. The space-time-varying uncertainty fields identify oceanic regions where improvements in data reconstruction and extensions of the observational network are needed. Poor reconstructions of pCO(2) are primarily found over the coasts and/or in regions with sparse observations, while fgCO(2) estimates with the largest uncertainty are observed over the open Southern Ocean (44 degrees S southward), the subpolar regions, the Indian Ocean gyre, and upwelling systems. Our estimate of the global net sink for the period 1985-2019 is 1.643 +/- 0.125 PgC yr(-1) including 0.150 +/- 0.010 PgC yr(-1) for the coastal net sink. Among the ocean basins, the Subtropical Pacific (18-49 degrees N) and the Subpolar Atlantic (49-76 degrees N) appear to be the strongest CO2 sinks for the open ocean and the coastal ocean, respectively. Based on mean flux density per unit area, the most intense CO2 drawdown is, however, observed over the Arctic (76 degrees N poleward) followed by the Subpolar Atlantic and Subtropical Pacific for both open-ocean and coastal sectors. Reconstruction results also show significant changes in the global annual integral of all open- and coastal-ocean CO2 fluxes with a growth rate of +0.062 +/- 0.006 PgC yr-2 and a temporal standard deviation of 0.526 +/- 0.022 PgC yr(-1) over the 35-year period. The link between the large interannual to multi-year variations of the global net sink and the El Nino-Southern Oscillation climate variability is reconfirmed.