In reply to ianstevens:
> I'm not an expert on this, but I think you may have asked a question to which nobody (i.e. "science") knows the answer.
My two minute google just now very much says otherwise, but it's hard to find a source dumbed-down enough for me to understand it. ;O)
So, since the OP hasn't hooked a biochemist yet, here's my take on it:
As the OP is talking atoms - the fat in your body that is being 'burned' is mostly made up of carbon, hydrogen and oxygen. And it is (kinda sorta) being burned - so it'll be mostly ending up as carbon dioxide and water. CO2 gets exhaled. Water - dunno. Presumably it just gets mixed up with the rest of the water in your body, and eventually finds its way into urine, sweat, tears or hot steamy breath.
Edit to add:
More googling..
Metabolising fat also produces urea, so presumably that'll be ending up in urine.
Bears lose 15-30% of their bodyweight while hibernating but don't pee or poo. Apparently most hibernating animals do, or the build up of urea would be fatal, but amazingly bears recycle the urea and use it to maintain their muscle mass. *Thats* my kind of work-out - sleep through the winter, losing shed loads of fat, and actually wake up with more muscle mass than you had when you went to sleep!
Post edited at 22:16