If you do a bit of searching on this site:
http://www.niac.usra.edu/...you'll see that there are several "flavors" of space elevators (God I hate that term). Click on the "Funded Studies" button, then scroll down a bit to find the space elevator.
What's listed there will plunge you into a veritable labyrinth of links to various ideas. It's very easy to get lost, but lost or not, what you'll find is absolutely fascinating, and it also makes clear that a space elevator can take many forms.
A BOAT
This one is pretty much as you seem to have in mind. The ribbons of the S.E. are anchored to either a large boat, or off-shore oil rig like structure. The advantage of the big boat as an anchor point is that the base of the S.E. could be moved so that the S.E. could essentially dodge things in orbits that intersect the ribbons.
Near the bottom third of this page:
http://www.isr.us/Downloads/niac_pdf/chapter4.html...you can see that at least one proposal places the anchor point just west of the Galapagos Islands.
Being completely ignorant of the implications of international laws, I'd imagine that the anchor point would be placed in international waters precisely to avoid international legal issues with regard to who has jurisdiction over at least the base of the S.E. to the extent possible, BUT,... you may be concerned with the wrong end of the S.E. in that regard, (more on that below).
A TOWER
Other proposals envision anchoring the S.E. on land at or very near the equator. But the fairly obvious problem there is having to deal with some kind of "Panama Canal" arrangement with a host country. It really wouldn't do to spend 40 billion to build the thing, then another 40 to 80 billion upgrading it to the point where it becomes a commercial shipping staple, and then have it nationalized by the host country.
A CHANDELIER
Actually, it isn't necessary to "anchor" the base of the S.E. to anything at all. The ribbons hanging from a counter-weight placed just beyond G.S.O. (GeoSynchronous Orbit), would have a very strong tendency to hang straight down from the counter-weight even without any "anchor point". Picture a chandelier hanging from a helium balloon for this one. The "helium balloon" would be the counter-weight positioned just past G.S.O., the chain suspending the chandelier would be the ribbons of the S.E., and the "chandelier" would be a space dock that hovers just above the atmosphere at around a hundred and fifty miles up.
The idea with this one is that you'd use a "space plane", or "single stage to orbit vehicle", to take off from an airport, you fly up to the hanging space dock, latch on, transfer cargo and/or passengers to "gondolas", that then make their way the rest of the way up the S.E. without having to expend the HUGE amounts of fuel needed to get that far out of Earth's gravity well by simply using a rocket to make the entire trip.
The problems with this approach are fairly obvious. For one thing, there's no way in hell that using a "space plane" to make the first leg of the trip is ever going to be as cheap as just using gondolas that run all the way to the ground. Another problem is that getting a space plane to latch onto a dock that isn't actually in orbit, but rather hanging from something that IS in orbit, would be fuel intensive not to mention tough to pull off from a piloting stand point.
But the advantages are a bit more subtle. For one thing, THIS type of S.E. doesn't necessarily have to be geosynchronous. In fact it wouldn't even have to have an equatorial orbit. You could put this type of S.E. in pretty much any orbit you want, even a polar orbit. In this case the "dock" wouldn't be in anyone's airspace, it'd fly over people's airspace the way satellites do now, and more than one country's space planes could access it according to a schedule determined by the orbit chosen. Not only that, but the orbit the S.E. inhabits could probably be changed as needed (although getting ANYTHING as horrendously massive as a S.E. to change orbits would probably be not only "a challenge", but dammed expensive in the way of the amount of fuel that would have to be expended to push something that big into a new orbit).
And of course you can see how you could play mix and match with all of the above concepts, an "airport" for example, that hangs at around 35,000 feet, placed in a NON-geosynchronous orbit where the "airport" moves at around 400 miles an hour with respect to the ground, which would be about a hundred miles an hour faster than the 500 or so miles an hour at which a jet liner cruises, making the difference in speed between an air liner and the "airport" close to the hundred miles an hour air liners travel at when landing. I.e. air liners fly up to the airport and land on it. A bit like landing in the middle of a hurricane I'll admit, but who knows? Something like that might still be feasible, and the real point here is that with a little imagination there are a lot more possibilities than could ever be covered in a single post.
LASTLY
As I said above, you may be looking at the wrong end of the S.E. when considering the legal issues pertaining to the placement of a S.E. Geosynchronous orbits are a relatively crowded place already with the many commercial and governmental satellites already there. Not only that, but a S.E., hanging from GSO, would also hang all the way down to Earth, and in doing so cross the orbits of things like the International Space Station on a regular basis, not to mention the orbits of hundreds to thousands of other satellites that aren't in GSO orbits. So who decides who has to give up the comfy orbit their satellite has been using for the last ten years in order to make way for the S.E.?
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