My fan character, Vertigo. Babysitting an Egg, waiting for some happless host to stumble on by....and get close and personal.
Ink on paper, color with adobe photoshop.
Aliens © 20th Century Fox Film Corperation*,
Nacronom © Giger*,
Art and character © 2004 Tina Leyk, All rights reserved.
-Giger owns the rights to the Necronom paintings that the design for the Alien was loosely based on.
20th Century Fox Film Corperation owns, without restriction, all legal rights to the Alien franchise, and anyone who wants to license anything related has to go through them. Dark Horse Comics has licensed limited publishing rights (i.e. comics, books) from Fox. Other companies have licensed the rights to toys, games, etc. But permission to do any of that comes from Fox.
Whatever rights Giger himself has to the Alien are those which he has by way of contract from Fox. IIRC he is allowed to create and sell certain types of Alien related artwork outside of the normal channels without recourse to 20th Century Fox. However, he does not own the copyrights to the franchise.