Most of the time when you see "conversion", it is converting a one-piece cue into a two-piece cue.
A prime example is taking a house cue and cutting it in half and "converting" it into a Sneaky Pete.
Titlist cues were Brunswick's most expensive one-piece cues when they were being produced, then they came out with a two-piece Hoppe model.
Many of the old school cue makers used Titlist blanks when they first started out making cues.
Old one-piece Titlist cues are pretty hard to find now and can be quite expensive if you find a nice one.
I have two Titlist conversion cues. One I bought new in 1973 and another I had made several years ago from a one-piece cue I picked up from Detroit. The one-piece cue I got from Detroit was made in the 1950s.
You can see the Detroit one in the following links: