Clint most times I toss my axe at the next tree to die, sometimes it even sticks (so far only when someone is looking...which is weird) I have a loop on my belt to pack it with but that seems to be more for the long walk in on a skid trail, carrying gas-oil, water, saw tends to take a whole bunch of hands, most of the stuff gets set somewhere more or less safe, but the axe goes with me to every tree. Stays at the stump while limbing and bucking, and tossed ahead to the next one.
you, may sometimes see folks carrying them in an aluminium basket type thing in the center of their back, not sure where to find one of them, seems a fair bit safer then swinging around in a hammer loop. Although I carry mine like that and its razor sharp, the only time I've cut myself with one (at least while logging...) was from a bounce back while pounding wedges, and I fall down alot... probably alot more then the rest of you...