Why do I get a taper when turning?

[BillTodd]

Can you support the end with a centre from the tail-stock?

Or, knock-up a tool-post mounted steady; just something to stop the work piece lifting (which can cause the tool to cut deeper as the work rolls towards the tool) and pushing away from the tool.

[edit] have a look at these: http://www.practicalmachinist.com/vb...ghlight=steady

I've checked the topslide movement relative to a test bar and the topslide runs parallel to the bar within .02mm over a 100mm length. Also the run-out of a test bar in my newly ground chuck jaws is less than 0.02mm over the same length.

Have you checked it on the top/bottom as well as the side? Height changes will cause your work to taper.