Private IP Networks

[#1]

Can someone explain to me how this comes about.
I have always understood there are three IP ranges assigned as private, meaning they are for use on private networks and are not routable on the internet.
These are:
10.0.0.0 to 10.255.255.255
172.16.0.0 – 172.31.255.255 and
192.168.0.0 – 192.168.255.255
Asbo Dog and others appear to have been allocated an IP address in the 172 range.
James said this.
Maybe someone can point me in the direction of some reading to clarify this.

[#2]

Think about how DHCP works on say, your corporate network.
The DHCP server can use MAC Addresses (or User Classes) to assign addresses to devices, and can recognise these devices no matter where on the network you connect them (a slight simplification, but true for many straightforward fully routed networks)
However, your IP Address is assigned not because of the MAC address of the hardware you use, nor is it determinable by circuit number (remember you can log on with your ADSL credentials at any PN-enabled line).
Therefore, another way has to be used in order for you to be given the correct address (and other info such as DNS addresses etc).
So, your username and password have to be used.
The mechanism for providing this is RADIUS, which is a vendor independent standard for central authentication - to communicate with the RADIUS server, you must have a valid address, so presumably you are assigned one on the RADIUS' private network initially, and as you are authenticated you are provided the correct details? (Or is the private range simply a function similar to APIPA where a valid DHCP Response is not received?)
In terms of the actual steps used on the BTw network, and the point where it was failing I can't elaborate [I don't know], but from summation I think one of the two is likely. (Or a similar variation)

[#3]

My guess would be that the BT systems are unable to contact the Plusnet RADIUS server to authenticate the user, which also means that they cannot retrieve the IP allocation details.
It's a bit like the Microsoft 169.x.x.x addresses allocated when a DHCP server is unavailable.
B.

[#4]

That makes sense. I wasn't quite sure where the radius server appeared in the chain.
I seem to recall a diagram somewhere of the path from user PC to PN systems and beyond.
Thanks guys