I agree that this is unprofessional behavior on the part of the other TA (let's call him X).
I understand your instinct is to try to help the students when they come to you, and that's certainly generous of you. Unfortunately, this sort of thing represents a very common pitfall for young academics. Working with students is very rewarding, in the short term: it feels like something where you can make an immediate difference in someone's life. This is especially true in contrast to research, where work is often solitary and progress is slow and difficult to discern. So spending extra time with students, while helpful in itself, has the potential to become a serious distraction in the long run. Balancing one's time between teaching, research, and other activities can be one of the hardest thing for an academic to do (it certainly is for me).
So I think this is a good opportunity for you to practice "protecting your time". Helping X's students, even if you enjoy it or feel the students really need it, is not something that can take priority over other tasks that are specifically your responsibilities (e.g. your research).
I would suggest having a talk with X and tell him that you're not going to be able to help out his students, and to please not send them to you. If you feel you need a justification for this, you can just say it's distracting you from your research or studies or something similar. If X's students keep coming to you anyway, you can politely tell them "I'm sorry, but I'm not the right person to help you with this. I'd suggest that you ask the professor during her office hours." You don't need to get involved any further; if lots of students start coming to the professor and complaining that X can't answer their questions (and in my experience, believe me, they will), or even that X sent them to you, who couldn't help: she will figure out that something is amiss.
I agree with the other posts that you should not explicitly try to play this to your advantage as far as getting the TA position. That seems to have the potential to backfire. It may work out for you in the long run, but stay at arm's length while things run their course.
On a side note, you mentioned that you've overheard X encouraging students to "copy their homework". I'm not quite sure what that means out of context, but if you mean X is telling them to do something dishonest like copy from each other without attribution, then this is a much more serious matter that I think obliges you to step in - it puts X over the line from unprofessional to unethical. If you feel you have enough of a relationship with X to speak frankly, tell him that's a bad idea: it's likely to get students in serious trouble, and also him if they tell the professor he told them to do it. Otherwise, or if X doesn't seem to take you seriously, alert the professor.