I'm sure it changes from country to country, but in the U.S:
Any piece of intellectual property is automatically protected under copyright law. If you write a poem and put your name on it before anyone else does, it's yours. Same goes for books, art, and anything else defined as intellectual property. You can trademark any original title so long as it isn't a single word (otherwise you'd be trademarking a word, which could cause some complications in use of said word). The creator owns the rights of a work and can do whatever he/she want with it, but if you want a filmmaker to make a book you wrote, you'll need to give him/her the rights.
What happens with screenplays is the screenwriter uses "options," which is where a film company buys the rights to a screenplay for a certain amount of time (usually about 2 years). In that time the film company can make a movie from your screenplay, but when it runs out you get the rights back and can option it to either the same or another company for another 2 years or so.
I guess the answer to your question is that you do not need to re-secure rights to your own work to adapt it.

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