Student wants to show everybody how much he knows
If the student is just overexcited and more advanced than others, then the  question linked above by ff524 has an excellent answer. However, that does not seem to be the case. By all appearances, the student talks to talk, and drops references to superior knowledge - real or imagined - to show it off. I've studied with plenty of students whose knowledge exceeded even advanced classes they were forced to take, and - in my experience - the common reaction of a true talent is boredom or eventually failing to show up, not jumping on stage. The closest case similar to yours failed his qualifying. 

Hence, I think your problem is one of learning to assert yourself in a challenging situation. Here are some suggestions for what you might want to try: 


Be an authority figure, not a friend. When I was a squad leader at the army, I was an unkissed geek-kid; my soldiers included a drug dealer, coal miners, and someone 10 years older, divorced, 2 children. I've found that, absent natural charisma which I don't have, acting somewhat reserved and distant, while always having an open ear for feedback, was the best way to get through this. When later TAing, I resisted the urge to fraternize and acted similarly, which worked very well for me (in both cases, I was top rated among my peers.)
Create a system of taking questions, and stick to it. This might be simple ideas such as one day taking questions front to back, the next left to right, etc. which - as students tend to gravitate towards seats in a particular part of a classroom - means your problem student will only get to lead a discussion every now and then.
Be professional, but honest about your frustration. If the student interrupts others, or you, first follow the advice of the linked question. I expect it to fail though as your student isn't interested in talking after class when no one witnesses their awesomeness. If it fails, tell them "I'm sorry, there are many questions others have, too, and I need to address theirs as well.(meet me after)" If you can't shut them up, keep eye contact, and say, more seriously but calmly, "I really have to move on. Please allow others to talk", etc. 
Seek advice from your professor, as needed. If the person becomes disruptive and unresponsive to your hints mentioned in 3., discuss with your professor, and ask if you can kick them out of a TA session when that happens. Express your concern about preparing the other students properly.
Assume good intentions, and talk with your student. This should probably be point 0. Ask the student if you can talk after your session. Be a bit flattering - interested student, knows much - then point out that others don't, and you really need to focus on them, and their more basic questions, while handling his in 1-on-1s, as necessary. This might clarify if they are acting in good faith and just get overexcited, or not.
Mention that TA sessions are optional, and that no one already having the knowledge taught is judged for not showing up. One of my TAs, stuck in a basic linear algebra II class with a 4-time math Olympics participant (b/s/g/g) who had gone through the entire Bourbaki already did this, and it was the last time the student was seen. If it works as in this case, you might also get a chuckle out of the other students who probably understand what you mean.


There is an additional informal way to address this as well. The next time you catch them being wrong in their aggressive ways, talk them into a corner. If they change topic, say so - "That's interesting, but let's not change topic. I'm really curious to understand what you meant when you said (X - the wrong statement)." Be calm, friendly and insistent, and keep this up until an error is admitted, or they shut up. As their interruption is only to show them in a gleaming light, it might help greatly in making it stop. I would only use this as a last resort though.