If you are talking about the string post, then they fall into a narrow range suitable for a peg head to be a total thickness from approximately 12mm thick up to 14mm thick. I predominately use the Grover Sta-Tite open geared tuners and my peg heads are at 12mm thick. They do have another model that looks quite similar but requires a 14mm thick peg head. It's really best to get your tuners in hand before committing to final dimensions.
BTW. I put a uke building class on quite similar to Rick's here in Cairns. Much closer to Singapore. Next one is July 2-6 with some spaces still available. The Cairns Uke Festival follows immediately after.