In general, you'd find the cables from the meter going into a junction box from which individual feeds were tapped to go to each fusebox.
I say "in general," because oftentimes you'd find smaller conductors piggybacked into the main terminals of an existing unit, or find daisychained boxes as you mentioned.
It wasn't uncommon to find extra fuseboxes in various places around the house, often the wooden type with a glass front panel.
I'm not sure exactly when the practice ended (it was a
little before my time
), but back in the 1920s and maybe early 1930s the utilities here charged a higher rate for lighting than for heat and other power. That resulted in two meters being installed and obviously separate panels for lights and sockets, although at that time the latter often consisted of just one outlet in each major room.