Hi Bob,
I've made a few canes myself (I have a bad back). I got tired having to say no to when people ask me if I made the cane I was using. See below for a pic of one.
Best way if you are turning them round or to size on your lathe is to use a steady rest to support the center. Several companies make metal ones - with Grizzly being about the cheapest I think (that's where I bought my metal one).
Another option is to make a wooded one. I don't think it has a partictular name, but I'm sure if you do a search for "wooden steady rest" you should be able to find the instructions. If you can't, PM me and I'll be glad to send them to you. Also attached is pic of the one I made. Other than the plywood, wingnuts and bolts, the only special parts needed for it are the rubber skate wheels. I found those at a local (big box) sports store.
Also if you are interested in getting other information or help with your cane project, there is a "stickmaking" forum that was a great help to me when I wanted to give it a go, as well as a guy that sells the "sticks" and metal accessories (accent rings & special tips):
The forum:
http://www.thestickman.co.uk/fourm.
The parts & other how to's:
http://www.hestickman.co.uk.
GOOD LUCK...John
John E. Brady
JEB's PENs
http://www.jebspens.com