I want to cite a book written by John P. Smith, Jr. Should I write
see Smith  for details.
see Smith, Jr.  for details.
I think my question boils down to: is his surname "Smith, Jr." or "Smith"?
I found the answer myself: this blog post (link) clarifies the situation. It says:
So my former option is the correct one. I should have
in my main text, and then "John P. Smith, Jr." in my list of references at the end.
For what it's worth from the perspecive of UK English we hardly use 'Jr.' at all. If we do, we would write it John Smith junior, though the non-capitalised contraction of jr. may be seen. It's far more usual to use forenames to distinguish between father and son, or between two unrelated people of dissimilar ages, though impratical if said forenames are unknown. In that case we're back to 'junior'. I have never seen 'Junior' used over here as part of a given name.