As the title suggests, how do ISPs, and other networks connected to the backbone ensure that their host network address isn't already in use by another backbone node, as there is no controlling device that governs them?
1If you mean there's no DHCP server to assign addresses, then the answer is that in most cases IP addresses of routers are manually configured according to the ISP's addressing plan, which should of course use only IP addresses assigned to that ISP.– jcaronFeb 16, 2019 at 0:41
The RIRs assign addressing to the ISPs. An ISP not following the rules will quickly find itself ostracized and cut off from the rest of the Internet.
IANA owns the addressing and assigns each of the five RIRs blocks of addresses, and the RIRs assign blocks of addresses from those to businesses that can prove they need them and are willing to pay for them. At least that is how it worked until IANA ran out of IPv4 addresses, then each of the RIRs ran out of IPv4 addresses. It still works that way for IPv6.
4Routers don't use each others IP addresses for the same reason you don't put your neighbors house number on yours: the collective society has agreed that your house should only have your number, and will ostracize you if you violate that agreement. Feb 15, 2019 at 21:35
If a carrier gave an IP address to one of its routers which is already used, and announced in the BGP tables, then any traffic for the correct destination travelling through the stolen IP address, will get swallowed up by the errant router. And as others have stated, would get a bit of a slapping.
However, quite a few carriers use private IP addresses, and since they are liable to be re-used, then that could pose a problem. It doesn't however, since they do not announce them. They are used on point-to-point links within the same carrier.
There is another issue though. A UK supermarket decided there were not enough private IP addresses available for their network, so they decided to use another company's public addresses. Not a problem, until we were required to connect to them. The network team ended up having to dual NAT it.
1This is very rare as most ISP have BGP filtering on all X points that prohibits their own IPs being advertised wrongly although it does happen Feb 16, 2019 at 4:05