Making a Custom Collet to hold a chrome part on a lathe

[Toolmaker51]

Theoretically and some visualization.
1 cut [not split] pinches diameter in 3 places at the opening, two adjacent to the cut and one at opposite side. It will only hold concentric if they are same size. The pinch can introduce axial loss of concentricity.
Splitting collet makes contact along length of bore, in same number of lines as sections made. Its radial & axial repetitive accuracy range is better if part size vary somewhat.
Interior shoulder could control part length, if stop is employed. If the collet has an exterior shoulder, that qualifies as a stop too.
BTW, tailpipe expanders are good starting basis for a spindle bore stop. Most times, I make a plug; bored slighty larger than stock being run. It should be longer than spindle diameter to not cock in the spindle. Then it butts against tailpipe expander. A real long rod of material might want a bushing midway.