Call it Monday Boredom, if you will, but a funny DNS question just popped into my head: if I were to, say, win the lotto and buy my own Island (which, of course, would technically be its own country), would I be able to receive a ccTLD for said island nation? Kind of like .joejohnsonisland or .jji?
If your island had a two-letter code assigned to it in ISO-3166, then you could petition ICANN to become the ccTLD manager, and have the corresponding ccTLD delegated to your nameservers. I believe all previous redelegations are documented on www.icann.org, so there's plenty of prior art to review there before wielding your hyper-platinum amex card.
If the nameservers were already present within the borders of the island, and your acquisition had caused you coincidentally to also become Supreme Leader and Ultimate Dictator, presumably you could just dispatch some armed goons to secure the ccTLD infrastructure and avoid the ICANN-wrangling part.
If your island had no ISO-3166 code assigned, then you would first need to talk to the maintainers of ISO-3166 to get it added to the list. If your island was not a widely-recognised territory or country, this might involve petitions to the UN.
If so, would the DNS have to be actually contained inside of said island? I think not, as it was mentioned earlier that .iq was run from Texas, but it's always good to ask.
There are lots of entries in ISO-3166 where the country/region/island/economy and its master server are not colocated, geographically. Sometimes this is a practical consideration (e.g. AQ is not hosted in Antarctica, since that'd be an expensive and inconvenient place for it to live) and sometimes it's a historical artefact (e.g. a pre-ICANN delegation, or a benevolent stop-gap until a delegation could be moved in-country).
Many developing countries do not have their ccTLD infrastructure deployed within their borders, for want of local skills, infrastructure or (often) confidence in running such services themselves. The Internet Society and the Network Startup Resource Centre (amongst others) expend a lot of effort trying to remedy these issues -- a local registry for local services can often be a useful catalyst for Internet deployment.