When someone changes their authoritative name servers via their registrar, what process does the registrar go through to update the top-level domain (TLD) servers?
Historically the root zone manager has taken updates from registrars through an e-mail template system. If you were messing about with NetSol 10+ years ago you'd remember the e-mail templates.
As inherently stable and reliable as e-mail is, Verisign (NetSol at the time) came up with a new RZMS (Root Zone Management System) which is actually just a set of specifications for a web interface to the database. The interaction protocol is call the EPP system (Extensible Provisioning Protocol; RFCs 3730-3735). Apparently this system is used at least for .com, .org, and likely many others. The TLD manager also communicates the status of the TLD Zone back to ICANN so they have what is essentially a backup copy (ICANN claims it's for verification and authentication purposes; like they would know if something was wrong).
A request is sent to the registry to change the authoritative name servers and the registry then pushes those changes to the root servers. The request is sent in real time, but it can vary by registry how quickly the root servers update.
Does that answer your question? Let us know if you need anything else.
Here's a layout of the process to become a registrar for .org (the .org registry is run by PIR):
And here are the requirements/business processes for Verisign-owned TLDs (.net, .com, and others)
It seems complex.