Damian Wayne is the son of Bruce Wayne and is currently Robin V. He is also currently under the tutelage of Dick Grayson as Batman.
Damian first encountered Steph when he saw her in the guise of Batgirl dispatching some thugs. Watching her from afar with Batman, Damian commented to Dick that Batgirl's work was sloppy, and (believing Batgirl to still be Cassandra Cain) wondered how this woman could be the same one who led the League of Assassins, or who Batman trusted to lead the Outsiders. Dick agreed, saying, "She's not as good as the other Batgirl." All of this happened in Batgirl (third series) (1).
Damian's distaste for Stephanie was only intensified on their first official meeting. Batman and Robin burst in while Stephanie was fighting the villain Diesel. They charged into the fray before Stephanie could explain that the bad guy bled gasoline, and Damian ended up on a puddle of petrol with the fiery villain. Ignoring Oracle and Batman's warning, Stephanie flung some ice disks at the pair. Unfortunately, she ended up freezing Damian along with the villain.
Damian did not take this well, later telling Stephanie that he hated her and wanted to stab her, which freaked her out and made her angry. He also mentioned that he would much rather have met Cassandra, because she sounded wonderful.
Later, Damian showed up at Stephanie's university. Francisco Gracia described him to Steph as the "little omen fanboy giving you the stink eye" and Stephanie promptly went to chew him out for almost compromising their secrets: "And you guys think I'm the screw up?" Damian dismissed her, claiming he was in urban camouflage mode. While drawing a Batgirl in the snow, he admitted he was trying to understand her because she wasn't uber-skilled and wasn't interested in vengeance. He couldn't see what use she was to anyone. Stephanie tried to explain that she and Barbara didn't want to inspire fear in people, but hope, but Damian continued to not understand. Stephanie gave up saying, "Of course you don't! You're ten! And stop staring at my chest." Damian replied, "What chest?" and Stephanie stomped off, grumbling "HATE" to herself.
Damian attacked Stephanie when he caught her eavesdropping on Batman and James Gordon. Stephanie wondered if it was "child abuse" to hit back at him, though she couldn't deny she wanted to, especially after he insulted her class status. Batman came over and broke them up, telling them they were off the case.
Steph finally let loose at Damian, saying that she had played grasshopper to Bruce's "Master Po" (Damian: "I have no idea who these people are") and that Bruce had trusted her enough to let her operated on her own. "How much did he trust YOU, Robin?" She immediately felt guilty for kicking a ten year old when he was down and apologized, but Damian admitted it was a good shot. Stephanie declared that they couldn't sit around waiting to screw up and they could fix this. She dragged Damian off to interrogate Jordanna Spence. She told Damian they would play "bad cop, worse cop" to which Damain responded, "I get to be worse cop!" and Steph said, "Attaboy."
They got the necessary information out of Jordanna- Francisco was bait to draw Batman in for Roulette- and Steph and Damian would have to rescue them.
Damian attempted to ditch Steph to rescue his mentor, telling her that he needed to stay "calm, cool, collected...and fast. You happen to be none of those things." When Stephanie tried to reason with him, he said ,"No girls allowed" and disappeared with a smoke bomb to get his motorcycle. Steph rolled her eyes at his ten year old behavior and followed him in her new batpod designed by Oracle. She cut him off when he called her a "dreadful shrew" and when he yelled that it didn't concern her, she replied, "Ladies first!" and motored ahead of him.
When they found Batman, Damian yelled at her to go high while she yelled to go low and she thought, "at least we're finally on the same page." It was a good thing she came along, because she ended up rescuing Damian when Dr. Phosphorus had a death grip on him- by crashing Roxy Rocket's rocket into the villian! She also had to help "little Lord Fauntleroy" take out Riot after she tended to Batman.
The pair confronted Roulette with Batman, Damian quipping, "Game over." Stephanie scoffed at him not to be lame, but Dick said, "Shh, he's learning."
Back at the cave, Stephanie and Damian had a civil moment eating waffles together, Damian complaining to her that the way she kept her hair out was a tactical error and bad for her secret identity. Stephanie rebutted that he didn't keep his hair tucked away either and neither do "Nightwing, Tim, Superman, Kid Flash, Wonder Woman...." She asked him if he wanted her to keep going and he scoffed, "Boring conversation anyway." (Batgirl (third series) (5)- Batgirl (third series) (7))
When Steph and Supergirl were captured by a Batman/Superman Robot, Dick made the robot drop Stephanie and Damian rescued her before she could splatter all over the ground, but while doing so he made a snide remark about her weight and called her "Fatgirl".
She and Damian took out Toyman, destroying his remote control. But it turned out Toyman was only a robot.
Later, Supergirl chastised Damian for insulting Stephanie, picking him off the ground by his cape and telling him he "shouldn't call girls fat! You shouldn't call anyone fat!" while Stephanie looked on with her arms crossed and Damian struggled, yelling, "Put me down!" (World's Finest (4)).
When fighting Ra's, Tim was kicked out a window and rescued by Dick Grayson. In the Batcave, Stephanie, Damian Wayne, Dick and Alfred Pennyworth congregated around him and waited for him to wake up. Steph noted that Tim's waking up, which Damian said was too bad, because it means he'll probably start talking. Steph asked Damian, "why are you so horrible? to which Damian replied "When did you start stuffing your costume?" (Red Robin #12)
Stephanie later teamed up with Damian again for a mission and began feeling more sympathetic towards him when she became more acquainted with the fact he was a bit damaged from not having a real childhood. She especially felt for him when he introduced himself as "Bruce" while undercover. The teamup went successfully, and Stephanie actually managed to persuade Damian to jump in a bouncy castle with her. She saw he was smiling and teased him about it, and he threatened to stab her as usual but continued bouncing.
In the miniseries "Gates of Gotham," Damian finally met Cassandra, and reverted to his form with people who intimidated him - he insulted and threatened her, until his own vulnerability at his father trusting Cassandra over himself became obvious. Cassandra's ability and maturity in the face of his hostility finally convinces him to trust her.
In the last issue of Steph's series, it became clear that Damian and Stephanie were now friends, inasmuch as Damian is friends with anyone. He came to check on her when she was at the hospital, and upon seeing she was fine, actually smiled and did a two fingered salute at her.
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