Indeed, I don't know how the Admin Mod's ascertain that a person is here under a false identity - but evidently they do figure it out rather quickly.
It seems the big indicator that someone was posting under a false identity is that, when the identity is banned, every trace of its postings seem to disappear as well.
I seem to be having trouble getting off of this topic, despite an earlier declaraton. LOL!
Probably duplications in the ISP packet info. Some sort of batch job might be scanning the data base regularly looking for such. I know that sounds CPU-intensive when you think about going through 80,000 items comparing them all to each other. The job can be low-priority so it runs in the background. Or maybe the mods only check (manually) when they get a ping or notice something themselves.
If a person uses a different computer and a different ISP in the second registration versus the first, I can't imagine how you would tell definitively.
Sometimes it's rather obvious, even without knowledge of IP addresses and the like. Medved, for example, has a habit of recycling the same material over and over again - which is what got him banned in the first place, actually - and so it's usually only a matter of time before something sets him off and he reposts something instantly familiar to people who know his usual style and material. Presumably the IP address is merely the final nail in the coffin, in that case ;)