Some languages mark the object as some kind of oblique, though. English has a phrase that is somewhat similar to it:
She is with child.Now, that is a rather special case, but illustrates the kind of marking I am discussing here. wals.info informs that this type of construction actually appears. Personally, I find some kind of instrumental marking to be very suitable for this (except maybe in certain specific types of phrases or under some circumstances - restricting this to non-human objects seems rather reasonable, for one, or some similar cultural restriction).
is.1sg cup.instr - "I have a/the cup"
is.3pl dogs.instr = "they have dogs"Furthermore, I find it reasonable that the instrumental case could be the case marking for any possessed noun - the instrumental case doubling as head marking in possessive constructions. Why instrumental? Well, there seems to be a vague correlation between using a thing as a tool and owning it.
The idea by which it becomes evident that I am a one-trick pony is this: reflexive possession of objects marked by the noun object being marked by the instrumental case.
He drive.past.3sg car.instr = he drove his own car
He drive.past.3sg car.acc = he drove a/the carAlternatively, the distinction could work like this:
He drive.past.3sg his car.instr = he drove his own car
EDIT: reading through the earlier posts, seems this is fairly close to another post in content. Meh. It is an ok rephrasing that may be easier to understand for people not that familiar with ergativity and such. Well, I will leave it behind and try to avoid similar embarrassment in the future.
He drive.past.3sg his car.acc = he drove his (someone else's) car