Basic biology should tell you that the only thing that counts for carbon capture is biomass added. Anything that the tree does that doesn't permanently add to its mass can't capture carbon permanently. Hence, once a tree stops growing, it stops capturing carbon. It still respirates because it does things that require energy, but any carbon it captures doing so is released fairly quickly again, e.g. when the leaves it produced in spring fall off and rot. Of course many trees keep growing a little even after they reach maturity, but the rate of growth is minuscule. A mature stable forest stores a large amount of carbon, but it hardly captures any more.