I was looking at a few integrated seat post designs, what kind of clamps they used.

This clamp looks innovative. I couldn't find a better pic that showed any more of what it was. Seems like a half circle, flat end against the bottom of the seat rails, that swivels to adjust angle. Then two straight bars on top of the seat rails, and by adjusting the tensions of those two bars, which one is pushing lower against the seat rails, it adjusts the angle.

Like I said though, I can only sorta see it and don't know what's really going on. If anybody knows more about this, or other innovative seat clamps i'd love more info.

It's an integrated seat mast, the frame comes with a good amount of seat tube extending over the top tube, and the user can chop it to the desire length then cap it off with a clamp.

I didn't know boat masts could cut anything...

I saw someone get there integrated seat post cut at the lbs. the seat and clamp comes off.

Are the masts pretty flexible in regards to the shape of seat post they will attach to, or is it a pretty standard and specific shape?

Better be damn sure you really like your saddle height before cutting! And don't change things like crank arm length. Plus it looks a bit funny to me, I kind of like the seatpost as it gives a "transition" between the saddle and frame.

I'm not into exact fit cycling enough to change my saddle height if I get cranks that are 5mm longer or shorter :s
The difference between the thickness of the soles of my 2 shoes is probably more than that.

As far as aesthetic, I despise the transition between an aero seat tube and a round seat post. I dislike even more the aero seat tube, round post for an inch, then aero seat post. It looks really stupid. Having the seat tube run all the way through to the seat looks clean and functions well

Some of them have a longer clamp so adjustments could be made in the future.

The part you're talking about is called the seatpost head. I've got a seatpost with a head like that. Very limited fore/aft adjustment due to the top rail guides (or whatever you call those) being so far apart but pretty good besides that.

Eastons have a similar construction.