If the adaptation is of a 'classic', where the originating author is no longer alive, where do you stand over the question of rights?

Hermyam- you could check and see if the said 'classic' is in the public domain. Usually according to US laws, any piece of intellectual property usually enters public domain at the completion of a set time limit since its first publication or after the passing of the author.

In other cases, the deceased author's estate retains all rights to his/her work and may even retain from releasing it to the public domain. In this case, you must approach the authors surviving estate and/or heirs/relations.

Yet there are other cases where the rights to a piece of work are just 'abandoned' and hence enter the public domain even without completing the time period.

Please see here for more details: http://en.wikipedia.org/wiki/List_of_countries'_copyright_length

Depends how old the item is. A ton of stuff is public domain now, since people have been writing for centuries. In a lot of cases, like with Shakespeare I believe, you're allowed to adapt the story, but you can't use a specific company's version. So like... I could adapt Othello, but I couldn't use the Longman Cultural Edition's exact copy, nor could I make it exactly like a Royal Shakespeare Company's production.

My college theatre teacher said the same thing. He had adapted Othello and it was one of the books we had for that year. Granted that was about five years now.