The original Bell Operating Companies (aka BOC and "Baby Bells") were formed when AT&T (aka "Ma Bell") was broken up on Jan 1, 1984. These were broken up through court action because AT&T was deemed to be a monopoly violating various anti-trust laws. Originally these new companies were granted exclusive rights to provide local service and in exchange they were not allowed to manufacture or sell telecommunications equipment; nor were they allowed to provide long-distance service. These restrictions were greatly altered by the Telecommunications Act of 1996.
As a matter of U.S. federal law -- set forth in the Telecommunications Act of 1996
-- The following companies are what consist of the Bell Operating Companies (BOC
Also included -- as a matter of law -- in the Bell Operating Companies is any successor or assign of any of the above that provides wireline telephone exchange service, but does not include an affiliate of any such company (unless the affiliate is included in the list above or a successor or assign of any of the above).
Each of the Bell Operating Companies were originally controlled by one of the seven Regional Bell Operating Companies. Through the years a few of these RBOCs were allowed to combine so as of 2019 we only have 3 companies remaining, AT&T, Verizon, and CenturyLink.