KTC means to Kill The Conversation.
People often times KTC when texting. Like when they reply back with pointless bullshit that you can't really reply back such as "lol" or "that sucks" so they basically KTC.
Someone might KTC you when they are too busy to give a detailed response or if your not worth their time.
Tim: Sup Stacy.
Stacy: Nothing much, you?
Tim: I woke up this morning feeling like shit, so I didnt go to school.
Stacy has just KTC.