Equity Research - Questions to ask when networking

1. What are you and your team known for? (some are known for modeling quarters with intricate detail, others are known for corporate access, long-term thought pieces, macro, etc.)
2. What are some themes your team is focusing on in your sector?
3. Ask about what the associates spend their time on. For context, some associates NEVER touch a model on some teams, and will just be little data monkeys running around gathering govt. data and making charts. Others have their hands on everything. Associates on my team do it all. In my opinion, makes it much more interesting than the alternative. 
4. What do you think separates a great associate from an average associate? (if you aren't worth the investment, your analyst or senior associates will see you as a resource to burn rather than one to develop)
5. "Any chance I could get a note or two, or maybe even a model, just to get my hands on something and maybe learn a thing or two?"

Hope that helps. Just show humility and curiosity. I can't speak for everyone in the field but if you try to send me a model you've put together, I probably won't have the time to look at it. If you send me a small piece of research (I'm an associate) then I'll probably read it and just write back my thoughts. My analyst will never read either.