We meet Yeoman Barrows in Shore Leave. Early in the episode, when Kirk complains to Mr. Spock that he has a kink in his back, she impulsively gives Kirk a backrub without him asking her to. He at first assumes it's Mr. Spock back there, but when he realizes it's Barrows he asks her to stop. That is the only contact we ever see between them.
Barrows beams down with Kirk, but she's not his date. Kirk soon dumps her to chase after other adventures.
Since this is a planet where everything you think about magically materializes, we learn that Barrows is apparently a very kinky gal who enjoys fantasizing about being raped by the likes of Don Juan. NOTE: Not by Captain Kirk.
Barrows spends most of the rest of the episode horsing around with Dr. McCoy. She shows lots of strong emotion to/about Dr.McCoy. She clearly enjoys his attention, weeps with seemingly sincere grief when she thinks he is dead, and acts jealous when he turns up at the end with two sexy android "Rigel-2 cabaret" showgirls.
McCoy divests himself of the showgirls for Barrows. Barrows is not, and never was, Kirk's girlfriend. If anything, she's McCoy's girlfriend.
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