in this industry, make no enemies...
The point above is important. NEVER burn a bridge. Aviation is a pretty tight knit organization, and you don't want ANYONE saying bad things about you. If you want to take some students with you, ask your employer before you do so. To do otherwise would be unethical.
Remember, your employer paid for whatever advertising he did, even if it's just the cost of rent at the airport. Students that came to the school and ended up with you as their instructor should remain with the school unless you have been authorized to take them. Remember that you also are not just cheating your employer out of some cash, but also your fellow instructors at the school who could have had another student.
Viewing the situation as dog-eat-dog, they screw me so I'm gonna screw them is NOT a good idea. Be the better man and do everything ethically. I'm sure many people here can tell you that when you meet another airline pilot, at least 3/10 times, you share a former or current acquaintance. If someone says a few bad (or good) things about you, it doesn't take long for word to spread.
Example, I was at a CAP meeting just observing, and I introduced myself to someone. A girl standing behind me who I did not know overheard me introduce myself and turned around and asked me, "Didn't you work for (Name of my old flight school)?" I said yes, and she told me that her instructor talked about me all the time. I did her instructor's CFI and CFII and we are good friends. The point being: your name can get around, so make sure nobody is saying anything bad about you.