A living tree removes C from the air and converts it into living tissue (cellulose, starches, glucose and other carbs).
When a tree rots in the woods, bacteria and fungi break it down. Some of that C goes into the ground, some goes into the air, and some goes into the bacteria and fungi. So it's not true that 100% of the roting tree's carbohydrates end up in the air. How much, I don't know.
When you burn wood in an EPA stove to minimize pollution, some of the C is turned into ash, some is converted into smoke which is then combusted in the firebox, and some is given off as smoke into the air or sticks to the walls of your flue on the way out.
If you are running a smoke dragon, more C is stuck to the flue and less is combusted in the firebox.
How much C goes into each place, I cannot say, but it if you really want to know the true answer, I think you have to measure C in all of these places.
When people ask me about liberating C and all that, I tell them I think my wood stove does at least as good as nature if not better. Some of the C in the smoke is combusted after all. Does that beat how much C bacteria put on their bodies when breaking down a fallen tree . . . maybe someone knows.