I have a number of these artwork cards drawn by the artists to fans. It seems that this form of fan appreciation (a note, a drawing and a signature) was most popular from the mid-1930's to the mid-1940's. After this period, the artists simply sent autographs out.
Burne Hogarth Fan Card
Here is some additional background information on Tarzan from Tarzan.com:
In 1927 Joe Neebe, an advertising man, approached Edgar Rice Burroughs with the idea of adapting Tarzan for the newspaper comics. At this time the "funnies" were just that ~ humorous cartoons like Barney Google or Mutt and Jeff. Others, like Little Orphan Annie, were similar to serials, with each day's adventure continuing on to the next day's installment. This is what Neebe had in mind for Tarzan.
Neebe hired Hal Foster to adapt Tarzan of the Apes for the daily newspaper strip. Foster would achieve his greatest fame as the creator of Prince Valiant, but at the time he started with Tarzan he was an advertising illustrator. The Tarzan strip debuted on January 7, 1929 (the same day as the first Buck Rogers strip). Foster managed to cram the first Tarzan novel into ten weeks (sixty daily strips altogether). Eventually this strip was published in book form, technically making it the first Tarzan comic book.
Foster's dynamic retelling of the Tarzan story was a welcome change from the usual comic fare, and soon newspapers across the country were clamoring to carry the strip. But if Tarzan in a black-and-white daily strip was something ~ wait until Tarzan hit the Sunday color comics! This debuted in March of 1931. First illustrated by Rex Maxon, after six months (and a lot of pressure from Burroughs) he was replaced by Foster, who quickly made Tarzan the first thing America wanted to read Sunday morning. All the wild adventure that Hollywood couldn't get into a movie was in full display in Foster's pages.
When Hal Foster left Tarzan in 1936 in order to work on Prince Valiant, he handed the reigns over to Burne Hogarth, who quickly made Tarzan into one of the most vivid and action-packed comics ever seen. His mastery of human and animal forms, the unconventionality of his layout, and his ability to make the images leap off the page earned Hogarth the title "The Michaelangelo of the Comics."
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Description: Original Artwork on Card Stock BURNE HOGARTH Tarzan signed "Dear Caspar: Glad you like the Tarzan Page. Here he is close up - and he signs his name -Hogarth- Best of Luck! December 1939," Note: The Burne Hogarth inked sketch is exceptional, and rare. Condition: Condition is Near Fine. [Item 6”W x 3”H] SeqID-0827 Updated: 5/21/2008