My site is hosted in the US. The domain was bought from an Indian vendor, and is being developed in India by an individual. There is no registered office or anything of that sort.
The site's content might be illegal in India, but is completely legal in the USA.
Is this website under USA or Indian jurisdiction, and how could it be moved from one to the other?
Websites are not ships that can choose a flag of convenience to govern which country's laws govern them. Generally speaking an analysis of which jurisdiction's law applies (which is strictly speaking a "choice of law" question as much as it is a jurisdiction question) isn't undertaken on a website by website, or business by business basis.
Instead, jurisdiction and choice of law are evaluated on a claim by claim basis. The owners of a website may be subject to some claims in India, to some in Bhutan, and to others in the United States, depending upon the claim. Without knowing who is trying to sue for what, you can't know.
Generally speaking, a business that operates in multiple jurisdictions, like a website, will be subject to the laws of all of the jurisdictions in which it does business in regard to claims with a connection to those jurisdictions. Of course, as a practical matter, only claims that can be enforced against the owners of the website are relevant, which usually means that only claims brought where the owners reside or own assets are relevant.
If the website owners own property or have amounts payable to them in India, there is a very good chance that India can, as a practical matter, assert jurisdiction over them. And, it is likely, as a practical matter, that Saudi Arabia or China would not be able to assert jurisdiction over them in a meaningful way.
The fact that businesses can be conducted through legal entities further complicates the analysis.
But, at any rate, the place to begin is to realize that the question "Under which country's jurisdiction does a website fall?" is basically a category error. You need to ask "Under which country's jurisdiction does a website fall when it is sued or prosecuted for X kind of matter by someone who lives in Y?" So, really, this one question is actually dozens or hundreds of questions that each have to be analyzed individually.
It falls under the jurisdiction of every nation state where it can be accessed i.e. pretty much all of them.
