Antoinette Kalaj was rumoured of starting a relationship with him while shooting the fourth movie of Pirates of Carribean. She played the role of a mermaid and began to date Johnny. A source claims that she has been seen having a dinner together with him once and that Johnny "would fly her on his jet to meet him." She was married and even though she denied of having an affair with him, then she divorced from her husband and it was speculated that it happened most likely because of Depp story.
http://loverofgossip.blogspot.it/2012/06/celebitchy_28.html
Here someone wrote and gave some information:
"It has been claimed Johnny had an affair with her whilst filming the latest Pirates of the Carribean, and that she would go on his private jet with him to wherever he wanted to take her even weeks after the film wrapped up.
Elsewhere it has been claimed that someone he had an affair with left her husband for him and she now expected him to do the same for her.
Kalaj left her husband a few months ago. So there you have it."
http://www.celebdirtylaundry.com/2012/johnny-depp-obsessed-with-amber-heard-ignoring-vanessa-paradis-demands-0709/