We’ve discussed this issue in several threads, such as here. A new study by a large group of researchers, recently published in Nature, looks at the ability of mature trees to absorb CO2. The conclusion is that “additional carbon uptake did not lead to increased carbon sequestration at the ecosystem level. Instead, the majority of the extra carbon was emitted back into the atmosphere via several respiratory fluxes, with increased soil respiration alone accounting for half of the total uptake surplus.”
An open-access companion article, “Mature forest shows little increase in carbon uptake in a CO2-enriched atmosphere,” adds perspective and discusses the need to additional research.