There seems to be three basic uses for hawks- recreational throwing, fighting/self defense, and bushcrafting. Most designs are at least moderately functional in all three, which is why a simple tomahawk makes such a great tool.
For a thrower: HB Forge Shawnee style-your basic 3.5-4 inch bit, thin head, slightly convexed grind with a rounded eye, no poll. 19 inch hickory teardrop profile haft.
For a fighter: prominant belly (that is sharpened to a slicing edge, if at all possible-hollow ground, even, maybe...) with a basic 3.5-4 inch edge, and a STRAIGHT chisel ground poll. I never really understood these hammer claw style polls, I guess they're contoured along a wide strike path? I'd just as soon take a simple arrow head shaped claw about 2 inches long and wide enough to be durable but not too thick and heavy to throw off the balance. The alternative is a rifleman's hawk style fighting poll. 23-24 inch hickory haft with teardrop shape.
For a bushcrafter... a flat striking surface on the back of the eye for hammering and a frontier hawk style head.
Now, as far as things like battle axes and field axes...
For field axes, a 2 pound head with a 32 inch haft, both single and double bit, the single bit with a square striking surface on the back. Makes life easy when you're beating on old stumps for fatwood or fishing grubs, or limbing dry dead branches.
Battle axes... well... there are so many amazing designs... I'd like to see a Coal Creek Viking Battle Axe though

I'd also like to see a functional mini-hawk-something short and light balanced specifically for throwing. Imagine a poll-less trail hawk minus about an inch on the length of the head, and a haft just long enough to balance it out for throwing. The idea is for a disposable combat thrower. In today's modern combat it'd probably be considered fodder for mall ninjas but I can just imagine a couple of Comanches running around with 3-4 of these little babies on their belts cranking them out faster than Custer can work his levergun. Another design I've been working on for my own purposes is what I call an "ulu on a stick". Basically a short belt axe with a full metal tang, wooden scales running the length of it, creating a useable chopper and useable ulu at the same time. Hawk thickness for the head, ulu shape and a thin convex grind-say 30 degrees inclusive, tops. Something that can be utilized as both a very classy looking slicer and food prep tool, and for light camp limbing. I drew a concept up somewheres, I'll try to find it.