Specifically, the circuit overseers have always directly interfaced with the Service Department and a specific desk at the branch. For instance, in the United States each desk covers one or more states, such as the Texas desk or the Florida desk. Some states have two as I understand it. So I would imagine that the arrangement wouldn't change. The district overseers basically were overseeing Circuit Assemblies, doing workweeks with the circuit overseers (typically the week following a Circuit Assembly) and doing PQRs (Personnel Qualification Reports - a kind of Annual Performance Appraisal) on the circuit overseer and his wife (if married). Also, they had some oversight responsibility for the Regional Building Committees (which are also going away).
I think (not sure) that the review/workweek function might be filled by "branch representatives" that just travel out from the branch. I doubt very seriously that the Governing Body will allow circuit overseers to float free without any kind of review. It may not be apparent but the more responsibility you have in the organization the more control you have to endure. You go from "high control" to "ultimate control". Things that you previously could not be counseled for sudden become fair game - you along with your family. It is hard to describe but if you understand how mid and upper echelon people functioned in the old USSR/Soviet Union then you have a fair idea of how it works in the mid to upper levels of the organization. Only in this case it is labeled "unity" and "loyalty". Better toe the party line or you'll find yourself discarded socially or worse removed/deleted and shunned - disfellowshipped without being disfellowshipped. I've seen it happen many times and I've watched it break men better than me.
CC