We would ask that you respect their privacy and that of their children during this time." Since then, the pair have collaborated on six blockbusters, including Charlie and the Chocolate Factory in 2005, Sweeney Todd: The Demon Barber of Fleet Street in 2007, Alice in Wonderland in 2010 and Dark Shadows in 2012.
But Bonham Carter said in October 2013 that the couple may not work professionally again, as Burton was "getting sick" of working with her.
It was an arrangement that raised many an eyebrow among fans, or at least in the media.
One explanation given by Bonham Carter, again half-joking, was that she could not stand Burton's snoring.
Although clearly a joke, those light-hearted words were taken by some observers as a hint about their personal relationship.
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A photo of Burton embracing the woman showed nothing more than "a goodbye peck on the cheek", the spokesman said at the time.