Remote Scheduling query


Hi all - first post so please be gentle! I've been reading the forums for the last day or so and the amount of information is overwhelming, in a good way.
So, apologies if this has been asked before, but if, with the customised firmware, my Hummy gets a different local IP address, will this affect the Remote Scheduling setup? I've already set up my box with a fixed IP address but at some point soon I'll be moving to BT Infinity and I think the routers they use have a different address range for the LAN.
Also, I appreciate the IP address the outside world will see will remain the same all the time I'm connected to the 'net, but what about any powering down of my router? This will give my network a different address...

Any thoughts?

The RS service uses the MAC address of your Humax, so it should not be affected.
I would have thought the Humax asks the Remote Scheduling website for information just like a browser does so the website doesn't need to know where you are or your IP address, it just returns the information that was requested back to where it came from and the router would track it and let it through to your Humax. The tracking is done as Brian says using the MAC address.
That is correct, The Humax contacts the RS Server, the Server never contacts the Humax so the server doesn't need the Humax's IP address