Early in my career as a fly fisherman, I was lucky enough to try out one of Kenneth Bostöms famous Rackelhane rods; in 1986 I bought my first. This rod have been the first option for big brown trout on 8 trips to New Zealand (1987-1997) and still is my number one rod when fishing in Norway for trout and grayling.
Today I make my own rods connected to Kenneth's philosophy; one third cane(trout grass) the rest graphite. I build rods from 7' to 13' salmon rods. Below pictures are from spectacular salmon fishing in river Orkla June/July 2009, where my 12'6" certainly was put to the test! The most pleasurable casting, best rods for thin leader tippets and the most effective fighting of fish, has always been the trademark of parabolic rods

Look what one of Europe's most experienced splitcane rod builders, Carl Anderberg, says:

"The word “parabolic” itself derives from the fact that the bending curve is reversed in comparison to standard action rods.
That is, most of the bending is forwarded to the butt instead of gradually increasing the bending from the tip, like in a “progressive” rod for instance.
This bending allows for interesting features:
The rod will respond quickly to the slightest movement and offer a maximum of leverage. So, you are able to start up casting with little effort and still get enough thrust on the line.
As the rod “kicks back“ from a very low point and transfer it to the tip via a stiff center it will exert an impact on the line  well after the caster has made his push. You get the feeling of an almost dynamic effect, which compared to common tapers seems to accelerate (of course it doesn’t). This thrust over a longer time is a great benefit; it helps to push the line through the wind and permits an easy line lift as well as smoothen out bad timing. False casting is reduced to just a few strokes as the rod works on the line next to continuously.

As a parabolic responds so easily it isn’t finicky about line weights (three or more line weights can be used) and consequently it will respond to a short line as well as to a long one.
It will cast with authority over all practical distances and be gentle on tippets at that.

Maybe all this gets you think a parabolic must be slow. Well ,You can throw a very slow line and let the line hover over the water but also speed up the line for a fast delivery; You can reach maximum distances in  three strokes.

All parabolic rods have one feature in common, the low butt power zone and the stiff center. But they don´t need to be all alike. "

Excellent splitcane parabolic fly rod blanks:

Here is some images of Paul Young original concept of parabolic one hand rods: