Did you know that J.R.R. Tolkien left no drawings of Gollum? It's true. Tolkien's publishers -- Allen & Unwin in the United Kingdom, and Houghton Mifflin in the United States -- published The Hobbit only with Tolkien's own hand-drawn artwork. Sometimes this was in color, and sometimes not.
The first anyone ever saw of Gollum was in Children's Digest, and American magazine that ran excerpts from famous books to get kids to read. The drawings appeared in February and March 1974.
Abrams was a graduate of the Rhode Island School of Design. He was a big fan of the British illustrator Arthur Rackham (1867-1939), widely regarded as one of the leading illustrators from the "Golden Age" of British book illustration (which lasted from 1900 until World War I). Rackham's work combined the northern European "Nordic" with the Japanese woodblock tradition of the 1800s. He illustrated famous editions of Fairy Tales of the Brothers Grimm, Gulliver's Travels, Rip van Winkle, Alice's Adventures in Wonderland, Aesop's Fables, Mother Goose, A Christmas Carol, A Wonder-Book for Girls and Boys, Fairy Tales by Hans Christian Andersen, and The Wind in the Willows.
The Hobbit was Abrams' first animated work. Abrams had graduated from the Rhode Island School of Design about 1970; he'd later teach there, and mentored many top comic book and children's book illustrators like Debra Valeri, Walter Simonson, Dave Lowe, David Wiesner, Trent Burleson, and Shelli Manuel. Abrams would go on to work on the Rankin/Bass version of The Lord of the Rings and the animated film The Last Unicorn and that's it. He is a well-known book illustrator.
Abrams' design for Gollum reflected Tolkien's text, in which he writes that Gollum has huge, saucer-like eyes and looks somewhat like a frog. Abrams kept the hobbitish body, but gave Gollum froggy legs and a distended, distorted face. Nonetheless, Gollum came off friendly and not very frightening.