The Key to it all

Thankfully there was a short break between last round and the semifinals, you weren't thinking clearly enough to fight right now. The events that just transpired were... hard to swallow and even harder to understand. You had reasonable evidence to believe your signature caused the odd behavior from Zane and Jean, but what exactly caused this power to appear? Honestly, there was only one explanation. Semblances often manifested in the middle of battle, especially stressful ones like the one with Jean in the back alley. You've heard stories of how Jean suddenly seemed to get a second wind in one of last years sparring matches against Caitlin. Similar stories were floating around about Zane and Lila, so why would the same not apply to you too?

But what exactly was this semblance then? A protective field around things you signed? If it was physical Zane couldn't have hit Infotracker earlier. So it must be mental, something that changed people's perception of things you "owned". Sitting in the locker room like this wouldn't help you figure out much more than that, you had to test it.
First you should try to sign something that didn't already belong to you. Looking around you saw a fresh shirt lying next to you, likely belonging to Ripley who was currently in the shower after his battle with Lila. You slightly straightened the surface and raised Infotracker next to it. You didn't want to permanently mark it, even if it worked, so you wrote "Property of Eugene Bluebeard" on the touchscreen of Infotracker and projected it onto the shirt. This solution wouldn't work for things you wanted to sign permanently, but it would let you test the exact rules of this ability. You were also curious how essential the signature was, which is why you left it out for now.

A few minutes later he came out of the shower, wrapped in a towel, and walked towards his spot on the bench. He suddenly stopped just in front of it as he saw your hologram on his shirt.
"Hey, uh, Bluebeard? Why's your shirt lying on my spot?" he asked with a hint of annoyance.
"Oh sorry, I though it was yours, let me move it over." you replied, curious as to what would happen next. As soon as you moved it away from under the hologram Ripley snapped at you.
"Why the fuck are you taking my shirt, asshole?" he grabbed it away from you angrily.
You disabled the projection, having learned what you wanted from it and let Ripley go back to redressing for now. So, people had to see the writing for it to take effect and it only worked as long as it was on the object. The signature was also not necessary it seemed declaring something your property sufficed.

Now, you did have an idea of how to use this in preparation for the next round. You grabbed your bag from below the bench which aside from water and some food also still contained your writing utensils for the earlier written exam. After some rummaging, you pulled out a pen and took it down toward the bench you and Ripley were sitting on. "This Bench belongs to Eugene Bluebeard" you wrote out along one of the planks. You were experimenting a bit with the phrasing, hoping that you could be more specific than your initial attempts. Sure enough when you nudged Ripley and pointed towards your scribble he got up immediately and apologized profusely.
"Hey, no worries." you assured him "You know what, if you help me out with something I'll let you sit on my bench, okay?". He accepted immediately, just as you expected. "Okay Ripley, I need you to tell me exactly what happened back there with Lila."
The normally relatively unsociable guy immediately brightened up. "Sure, I can do that! While my memory got a bit unclear towards the end I remember that I couldn't move once I looked at her cleavage. Not because I was nervous, I physically couldn't lift a finger, y'know?" That made sense, even the biggest pervert wouldn't freeze in the middle of battle because of some cleavage alone. Ripley continued "And then when she was right next to me she whispered that I'd get a huge erection and then walk out of the hall. Don't know how exactly she did it, but my body did exactly what she asked. Fuck, that's shits gonna haunt me for years. But yeah, that's all there was to it really." Ripley sat down at his spot on the bench, as you allowed him to do so after helping you. Returning to your thoughts you tried to figure out Lila's method.
It seemed like she had some sort of Mind Control tied to her sexuality, which explained her outfit. Was it specifically her breasts, or just looking at her sexually? This might be why she didn't use this ability in round one. Her opponent there was a girl that, from what little you knew, had a boyfriend.
If you looked at her with attraction or sexual thoughts it gave her control over your body, so you'd have to avoid looking at her as much as possible, right? Well, you had a different idea actually. Taking out your pen again you pressed it down against your forearm and wrote "Eugene Bluebeards body". There, if your semblance worked on people she could no longer harm you as soon as she saw your arm. All you had to do was get close enough for her to read it and then beat her. If it didn't work you'd effectively have to fight blind but if this DID work out, you might have a shot in the finals too.

Actually, who was Caitlin fighting in Match 1 this round?

Yeah, you had a pretty good guess that you'd face her in the finals.