What happens to routed troops?

I just read in the Gamespot guide to RTW that any AI soldier who routs off a battlefield turns up in another AI army. Is this correct? When you smash an enemy army, the stack on the campaign map just disappears - are the routed men who make it off the battlefield put in another nearby stack? I'd assumed they just melt away, rather like the Iraqi army after the Americans took Baghdad.

I kinda hope the answer is yes. One of the things I liked about STW and MTW was the way you needed cavalry to pursue routers and avoid fighting them again. It captured the dictum (Napoleon's?) that no battle is decisive without cavalry. So far I've been assuming that AI units that disappear following a decisive victory and so the cavalry pursuit on the battlefield seems rather less important. But the Gamespot piece has made me question that assumption.

If enough soldiers survive to allow a unit to remain coherent, sometimes any surivivors will allow a unit to continue particularly if the remainder of the army is victorious, the stacks seems to survive. If the battle is one where one side perishes - most city battles - they seem to vanish into the ether.

Yes, I understand that in city battles, the routers disappear - fair enough, they have no where to run. And I know that sometimes if enough of an army survives, the stack can survive. My question is whether, in cases where the specific stack dissolves, routers can still turn up in other stacks further away? Maybe it is just poor phrasing, but the Gamespot guide seems to suggest that.