What are the tops of mountains such as K2, Everest, McKinely, etc. like? Does it come to a point at the top where only one or two people can stand. Is it more like a rounded hill top where a couple hundred could fit?
I think they’re all different. Everest, in particular-- I’ve seen pictures and read accounts of at least a half dozen or so people being up there, and I’ve never heard of anyone falling off.
The one “large” (by continental US standards) mountain that I’ve “climbed” (if you can call it that-- it’s more of a hike-up) is Humphreys Peak. The summit of that one must’ve been at least 15’ x 40’ (from memory), but I get the impression that that’s unusually large.
Pointy?
They vary a lot. Plus it depends how picky you are about “the top” - is it anywhere you can stand so your head is above the top of it, or is it the very topmost point of rock, which might be a small boulder?
With snowcapped mountains, like Everest, the summit can be always changing, because often there is a cornice of windblown snow on the top. You might not even be standing above solid rock (so be careful!)
The famous shot of Tenzing Norgay on the summit of Everest, taken by Edmund Hillary, shows it to be pretty pointy. I could nitpick and say he’s standing at least a foot below the actual highest point, too!
Other mountains can be pretty flat - sometimes to the extent that you can be wandering around for ages trying to locate the highest little bump in a peat bog. I speak from experience of British “mountains” here. 
More pics: Mt McKinley
K2 - are you going to go up the last bit or what?
Note that it’s easy for a camera’s view to be a bit distorted - those guys may have been on the true summits.
I agree that camera angles can easily be misleading, but you can see from the postures (one leg bent, so one foot clearly well above the other) that they are standing on the slope in these cases.
My real experience is in Tibet, where with the extreme day and night temperature variance, the rocks fracture. That means even at the relatively low elevation of 16-17,000 feet, it’s pretty damn pointy at the top of the dozens or so peaks I’ve climbed. Nothing like a big table where you can lay out like say the top of Mt. Lassen (but that’s a volcano so really a different animal).
Haven’t been to the tops of the peaks you’ve named, but I’ve been to other less famous ones. Mount Adams (Washington State, US) and Mount Shasta (California, US) each have a mound at the top with room for maybe a couple dozen people to huddle close, but that mound is on top of a more gently rounded hilltop.
Go to the top of Half Dome in Yosemite National Park (California, US), and it’s more like four football fields, a broad flat area.
Pikes Peak (Colorado, US) and Mount Washington (New Hampshire, US) both have large flat areas on top, with plenty of room for a parking lot, gift shop, train station, and weather monitoring equipment.
Everest summit photos mostly show people standing on a narrow sharp point, one or two climbers at a time, but I haven’t seen a wider shot that shows what’s immediately below them. It’s possible that the point on which they stand is only a few feet above a surrounding plateau.
Google Earth might show you what’s what. Fire it up, fly to the mountains in question, and have a look-see.
Well, my local mountain…
Sandia Peak on the edge of Albuquerque in New Mexico is a spectacularly vivid example of something you’ll see to a lesser extent at the top of lots of other mountains:
instead of a rough but uniform terrain rising up to where you stand at the top, you look in one direction and your eyes tell you that you are looking across smooth flat level ground. It’s just that all that smooth flat level ground is tilted up (in your direction) at a significant angle! And then, right there where you’re standing, that’s where it got ripped loose from the surrounding countryside, like the Jolly Green Giant had taken a pancake spatula and jammed the edge into 500 miles of flatland and lifted. So when you look in the other direction that’s the ripped area, the chaotically jagged terrain where the land under the original flatland was brought up from under the surface by the forces that lifted this area. Or by the Giant’s spatula.
And of course the highest point is rather disappointing as mountain peaks go…
Been breakfast cooking today?
What, no sausages?
So are you considered to have successfully “climbed” the mountain if your head is above the highest point, or do one (or both) of your boots have to be on the hightest point?
I don’t think there are a lot of nitpickers on mountaintops. They’re all tied up on internet messageboards :).
One way people prove that they reached the summit is to take pictures in all directions.