Activating the iPhone in 'not-my-PC'?

Ok, my english sucks so...

I'm in vacations at Miami. Yesterday I bought a iphone oob 1.1.2

I would activate it, but I would have to do that at my cousin's PC. If I do it on the PC of my cousin, when I want to connect the iPhone to my PC (at my house) I'll have any problems with the iPhone?

no, you will be fine :) It will just say about having a profile on another machine, just create a new profile.

Oh, really? Great. Thanks for answering, btw. :)