That is to say, in the unlikely event a modern passenger vessel founders prior to the arrival of external authorities and rescuers, or the survivors at least are left ashore any significant length of time before these show up, how encompassing is the captain’s authority under maritime law, and is it affected by the laws in place on the piece of land they have landed on? There is no terra nullius outside Antarctica that I can think of, everything is now recognized as belonging to someone or being in dispute between known parties. Does the captain’s authority over passengers still extend as far as authority over crew, as once it did? The crew’s authority over passengers? How has the captain’s authority over crew themselves changed under emergency circumstances.

My suspicion is that modern international and national law and, at least, jurisprudence, may have said quite a bit.

Traditionally, I suspect that the captain’s authority continued without interruption or limitation, in whatever the same form as shipboard, until the arrival of superior naval, military, company, or civil authority.

I am unaware of specifics, but I would note there was a lot of practical precedent for the authority of naval officers in far flung places ashore, over their crew, and passengers, and sometimes their nationals in general, where no higher national authority existed and as the sole representative of their national, sovereign authority. Especially if not only in new lands or otherwise uninhabited ones, or where the local authority was not presumed competent to be in charge of one’s own. This could be more a British than American thing, but I would be surprised if early American sailing navy officers in the Pacific and Asia, or the Middle East, did not act on a variety of implicit diplomatic, consular, gubernatorial and police powers when the only possible on scene authority.

Certainly Royal Navy officers would on occasion find themselves the only King’s or Queen’s representative on shore, even given Britain’s early commitment to have quite a lot of civilians scattered around.

I have never read anything by anyone claiming to be an expert on this specific matter, so anyone with citations welcome.