Where are the world's Established core routers situated? On which major protocols do they run?
This may answer some of your questions:
Top level routers are called core routers:
I assume the top level ones are owned by the Tier 1 companies:
Level 3 Communications, TeliaSonera International Carrier, CenturyLink, Vodafone, Verizon, Sprint, and AT&T Corporation.
You would also want to look into BGP protocol.
Border Gateway Protocol
The main thing to wrap your mind around is that this is used to route blocks of IP addresses (Called Subnets or Supranets) instead of individual addresses. To get your feet wet you would want to try using an AS Lookup tool.
BGP is used to cross from a network owned by one company through to a network owned by another company, or a major subdivision of a very large network within the same company. So this would get you to the core router, and would be used between two core routers on two different networks. The core router itself might be running ATM, Frame Relay, OHC, SONET, X.25, X.75, ect, from core router to core router within its own network.
Separate names with a comma.