As a followup, I called the county tax appraiser.

He first provided a glib response that nobody taxes residential
propane tanks. They ignore them on sight. Ummm... OK.

I then asked for an upgrade to the person answering, and got a
county *residential* adviser who first tried to convince
me that a tank is a repair, and as such is not taxed.

Allright. I asked for another guy - but I was stuck with this
one.

It took me a while to get him to understand that replacing
a rented tank with a rented tank, or, replacing an owned
tank with an owned tank isn't what I was asking ...

The tax question I was asking was:
Q: What is the residential tax consequence when a rented
propane tank is replaced by an owned tank (costing
roughly $3,000 to $4,000).

He said he'd get back to me.

PS: If someone is paying taxes on it, that's part of ownership
(in California, taxes are part of the adverse possession clause).