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You aren't actually reregistering the modem. You are just changing the device connected to the modem i.e. the computer. The ntl network, through the modem when it gets powered back on after you change the connection over, realises it has something different attached to it and issues the new connection details of IPs to the modem, and thus the modem to the new computer.
Thus it is the computer, not the modem that is the controlling factor. You can connect a number of different things to your modem, but only one of these at a time.
It's slightly different for users of Set top Boxes, where there is a formal registration proceedure needed for each new computer or device that is attached to the STB.