The address space is scarce (not dissimilarly to ipv4). Ethereum is used to map address space to owners and activities like transferring ownership. Urbit processes listen to an Ethereum gateway to learn about ownership changes and address lifecycle events ("breaches"), there aren't other "transactions"/fees involved in the protocol/implementation.

This part of the project is called Azimuth - and can be used for other things: https://github.com/urbit/azimuth