Well, according to what I observed, I built an Airport corporation and made it contract full production to the country. When I checked back up on it, it made a sale (cash jumped dramatically) and I saw an airport on my country map.
Unfortunately, it has since disappeared. However, I don't have an Air Transport company.
on your country page, click on map customization and see if the airport shows up there. If you see it, make sure it has a check mark in the box beside it, if not it will not show up on the map. Also, if it is checked the country map may be conjested and it may not show up.
I remember it showing up above my military units when I clicked "Customize Map". I remember only renaming it when I had it. It was checked when I had it.
Its no longer in my country. I really don't know why it would appear from my Airport corporation and then disappear. I can only wonder if it has something to do with the Air Transport corporation, or even other supplies.
Its all very confusing, especially because I wasn't able to find anything about it in the manual.
Well, I believe that airports are tied to air transport corporations. Like normal corporations have a little corporation target, but air transport corporations have a corporation target and an airport target. That's how it used to work.
The only thing I can thing of that an airport could do is to provide more airports for sending disaster relief.
Haven't bothered checking the first recently, and I have never bothered checking the second.