I have Ovi Maps on my Nokia 5800 XpressMusic (V 31.0.101.478.01). I have downloaded all the maps of Europe and explicitly indicated in the preferences that it should run offline. Nevertheless it goes online almost every time I turn the navigation on. It is just a few kilobytes every now and then but anyway quite unpleasant when abroad.
I see it in the log of the GPRS connection.