The main thing that's kept me from getting an axe or tomahawk is that they are extremely destructive to the target.  I use pieces of 2X6 nailed to a frame, and they can rapidly destroy these...

I have done some throwing with a very similar weapon, a big meat cleaver.  Technique is the same...

A very "slow" motion that comes fromt the shoulder.  The thing is heavy enough you'd hurt yourself otherwise... Just let it naturally turn over and adjust your distance till you're getting that front-corner "stick".
Someone makes a very small throwing "hawk", and cheap too.  Saw it on Amazon for only a bit over 20 bucks.  Might try one.

The throwing hatchet is a classic example of bad engineering design.

The purpose of the handle is merely leverage for a strong throw.  It is the head that does the work.

But here we include an awkward heavy handle WITH the throw.  Dumb, dumb, dumb.

The handle adds weight that has no value, and adds a huge dimension where the head can't stick/cut.

The solution though is simple. 

Don't throw the handle.  Swing the handle, let the head fly off.

I have one of those as well. I found the handle to be too narrow so I wrapped it with some Amy Digital Camoform wrap. It's now much more comfortable. I ususaly use a wood pile to throw it into, just get a few of the logs and point them towards you and it works pretty great. I threw a lot of mock weapons as a kid so I think it realated to my success now. I almost never have issues with mistaken rotation. The motion feels very natural and whether I throw really hard or lightly it usualy works however I throw. I also throw with 2 or 3 rotations in which the percentage of hits goes down drasticaly but the satisfaction is much greater.
I am not near as good at knife throwing but that's okay as the throwing knife really isn't all that effective for combat under anything less than master status.
Also, the SOG is a general purpose combat tomahawk, which can be thrown. This is a "throwing axe"
http://www.amazon.com/Gil-Hibben-Professional-Throwing-Axe/dp/B000W3U5HS ;

I also sharpened the spike on the back which comes almost rounded and I now I usualy throw it spike first because it preserves the edge.

I use a section of tree trunk about one foot (35cm) thick, as large as I can find and roll out of the woods.  I nail  two 2X4's so the top edge is chest height.  I nail a large gate hinge to the back and another 2X4, this forms a tripod, the target will last a couple of years before you beat it to pieces.  And for some reason, all the right handed throwers hit the left, as you face it, leg, so you will need to replace it about twice a year. 

You want the target thicker than the nails or screws holding the legs or you will notch the edge of the 'hawk when the target gets chopped up and the edge starts sinking in pretty deep.

i own the same hawk.......thow i dont throw it, i do use it, and my only complaint it that the edge is to thin and can bend with use
i have had to work the edge a good bit to get it back into shape.

Nomenclature not withstanding, I'm proud of you, Rat Man.
You found by natural inclination what my of my Boy Scouts could never get.
Congratulations.

Throwing (chopping edged implement): Ax, Axe, Hatchet, Tomahawk.
What it's called may depend on what word is common to the culture describing the tool.
I always simplify with "Hawk".
What Hibben calls a "Professional Throwing AXE", I would call a hatchet because of the length of the shaft.
What I make is 20" long and has a 2-Lb head. Not really your standard issue Indian Tomahawk but just right for my size: 6-2, 220.

But back to what Rat Man said:
The key is to relax and not try to make it do anything.

For the record: I've found what may be the best comercial throwing Hawk: the 16" Estwing Campers Axe.
(below)

Please try one before you knock it. This is a real thrower.

ChuckRocks

Very impressive, Michael.  I was hoping to see you throw a U.S. Amry E-tool (an excellent tool/weapon) but I guess we can't have everything.