Alternately, the dependency can start its own supervision tree with any global processes/tables hanging off it from the beginning; and then export a Mod:start_link/1 function which clients will call, which will 1. start a child tree owned/managed by the dep's supervision tree; but which then 2. links that child subtree's root into the caller as well.

Such deps are integrated, by adding a stub GenServer that calls Mod:start_link/1 in its init/2 callback; and then adding a child-spec for that stub GenServer in your client app's supervision hierarchy.

The ssh daemon module in the stdlib works this way. Most connection-pooler abstractions (e.g. pg2, gproc) do as well.