No smaller than 12.5mm.
For years I played with a 14mm. Every cue that I have ever had made for me was that size up until recently when I came back to pool and bought a few cues that were already made and of course they weren't that large.
I would probably still be playing with my 14mm shaft except I had the cue refinished and after 30 years it had to be sanded down a bit in order to make it like new and even out the spots where it had worn down a bit from play over the years. It is now 13mm.
I learned to play with a 14mm from Jack Taylor.