If I read you correctly, you just did propagate it. Remove the rooted leafy
stem and the log will produce another.
Your plant is Cordyline terminalis.
Here are a couple of links with info on how to grow it.
David Nornan Hare <pixiedave at mindspring.com> wrote in article
<7r17dp$idh$1 at nntp8.atl.mindspring.net>...
> I have a 5 year old Ti plant that I started from piece of root/trunk that
> came in a blister pack from Hawaii. I shaved the wax of the ends and
> an eternity until roots appeared. The plant appears to be healthy. My
> question; How would one go about propagating this plant. Is it old
> , would I cut and section the trunk and soak like original piece. Will
> root and stump survive and put out more leaves Ect? Thanks