Are you interested in the liability for damage and contamination or the ownership? Either way there are holes you could drive a bus through.
Most importantly in what follows, please bear in mind that I am not a lawyer. However it is edifying to recall that barristers are in aggregate wrong 50% of the time by definition, as it is an adversarial role with a winning and losing party. Hence any of the following could be on the nail, or not!
There is the Outer Space treaty (1967) and the Space liability convention (1971).
Liability
The liability convention is clear on the idea that a space object includes its launch vehicle and that the launching state (notoriously poorly defined):
"shall be absolutely liable to pay compensation for damage caused by
its space object on the surface of the Earth or to an aircraft in
flight."
A "space object" is defined in the liability convention:
includes component parts of a space object as well as its launch vehicle and parts thereof.
Hence this appears to include first and second stages of launch vehicles and perhaps carrier aircraft and rail-mounted rocket sledges too, these weren't defined.
- It also says nothing about about the damage caused (e.g. leakage of toxic or radioactive material) under the surface, within the oceans. I mention this simply because the oceans are referred to in the question.
Ownership
The liability convention says nothing about ownership, e.g. for salvage. The Outer Space Treaty does touch upon ownership and says:
A State Party to the Treaty on whose registry an object launched into outer space is carried shall retain jurisdiction and control over such object, and over any personnel thereof, while in outer space or on a celestial body. Ownership of objects launched into outer space, including objects landed or constructed on a celestial body, and of their component parts, is not affected by their presence in outer space or on a celestial body or by their return to the Earth.
However the Outer Space Treaty does not define "objects launched into outer space" so well. It appears that it does not obviously include non-orbiting rocket stages to the extent that they are not "launched into outer space".
Whether these are considered abandoned from an ownership (not liability) perspective would have to be checked against other forms of law, national or international, and whether that even mattered for salvage, according to whether the object landed in national or international waters.
What is more, even for objects launched briefly into space and then returning it appears that there are two sub groups:
- Registered objects, which apparently are permanently subject to jurisdiction and control
- Other objects are simply "unaffected by their presence in outer space / return to Earth" and thus can apparently can be abandoned in the sense of customary law.