Willows have a 1 in 8 chance of depleting when receiving a log, and a respawn time of 8 seconds. A roll to receive a log is done every 4 game ticks when chopping. The chance to successfully chop is affected by the axe used and Woodcutting level, better axes and a higher woodcutting level increases the likelihood of successfully receiving a log.
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There are several mentions of willows by people around Gielinor as well as in books. The following text is transcluded from Gielinor's flora - trees. The information found within the book is more often than not just flavour text, and does not reflect their properties or uses within the game itself.