As I said, it is unlikely that BP will go under, but it is a possibility. Another thing that could happen is that BP shares will drop so low that some other oil company will acquire it. The BP name is no longer worth sh*t. That "Beyond Petroleum" bit never flew, anyway. It is rather likely that BP will be acquired, merge or in some other way be known by a less despicable name.
When BP (as in British Petroleum) bought out Amoco (as in American Oil Co.), they had signs at the station under the BP logo, stating that BP sold "high quality Amoco Gasoline" ir something like that. After a year, the signs vanished. I guess they were worried about a boycott of Americans who did not like Her Majesty's country taking over something American.
