🚀 go-pugleaf

This is a very good explanation, but it's very different from anything
I've understood.

I own property in NE Alabama, in a sparsely-settled county.  In that
county, if several people share a road on private property, they request
of the country that the road become public property.  At that point,
they loose the right to deny access, but gain free road work, sometimes
even a paved surface.  At the same time, if a road is no longer being
used by several families, or if alternative routes exist and the county
no longer considers the cost justifiable, the county will close the road
-- I believe after a public hearing -- and the owner is then free to
erect no-tresspassing signs, which almost always happens, as a few
individuals will try to continue to use the road (in cases where no
signs have been erected, the roads remain passable to four-wheel drives
for many years).  Certainly, people with property along such an
abandoned road could still assert their use of the right-of-way; other
people can pass only if the owner doesn't mind.   A friend of mine owned
property with a road his family constructed traveling through it to a
popular "beach" on a river.  When people started using the road to dump
trash, he closed it, and then he had people arrested who broke down his
gate.  They argued that the road was public right-of-way since it had
been in use for many years; he argued that it terminated on his property
on the river, and the river was not a navigatable stream, and won.

Thus, I would tend to identify a public road by who was paying for it. 
Your clarification would be helpful.