two company's > sharing domains?

>I recieved a call from a company that says that in their network places they see our domain name with only one PC inside the domain.  this is wierd becasue we have no connectivity between the two locations.

I would be curious as to who called you from this company (IT or user) and what your role within your organization is (IE. Network Admin or other).

>SO the question is how in the workd is it possible for this to happen?  in our network there is absolutlely no sign of them or any other doamin.

My guess would be that there is possibly a test domain set up on their network. Does your company have any affliation with them?

>If this user( the one that shows up in their domain) was on there network would it ne possible for this to be the way it is?  how would they remove our domain name from theur network places????

Have you verified that this user (Your user that is on their network) is in fact an actual user of your domain?

LOL, i found out that THEY have an unsecure wireless access point and XP on the users PC continuosly connects when the user is in the area...

One of your machines attached to their wireless? You may want to configure your wireless enabled machines to NOT connect to any available WAP. This could result in one of your machines attaching to a hackers WAP and expose your data.

Ive seen that before with wired networks. A vendor or something will come to give a presentation and hook their laptop up to the lan to get internet access then their workgroup shows up in network neighborhood for a long time.