Pitching A HF Something They Already Own

Not a good idea because, as you mentioned, they will know far more about the name than you do + it will sound lazy, like you just looked up their holdings and threw a dart to decide which one to pitch. Pitch a different name, but if you've researched one of their names, you can bring it up and mention you'd like to discuss it further. 

1) Not to be too semantic, but keep in mind the 13F just says what their holdings were last quarter, not real-time. Not to mention all the nuances that come with any schedule 13 filings (A, D, F-HR, G, the amendment filings).

2) I think the idea of pitching why to add on to a position with strong research can be a good idea. Or the other way since you are talking L/S. If anything, it shows you've made an effort to learn the fund and their investment approach outside of the boilerplate they put in their GP's or LP's prospectus. But you definitely have to come correct and make damn well sure you've done all your homework and have the evidence to show how you got there so you can show your work. That way even if they entirely disagree, they also at least see you've put real effort into it and come away with respect for that level of DDI.

3) The PM will know plenty about the security, but it'll fall down to the associate and analayst to really know the ticker inside and out. So if you can handle them well, diplomatically, professionally  and impress the PM in the process?

If anyone wants to counter with their own A2D, I'm all ears.

Just pitch something they don't own

1. They are always down to hear a better idea that can replace an existing position in the book
2. There are many ways to impress them - why take the hardest path (when the PM / analyst knows the name inside out)? 

Pitch a short on one of their long plays. PM will grill you, but he prolly wont forget about you either haha

Talking about stock pitches, would you pitch a stock in the interviewer's sector even if it's not yours to show that you did some research? 

I'm currently covering TMT, interviewing for an Industrial pod, and they told me they were not looking for an already expert. 

Also, is it industry practice to pitch the same trades to different members of the same team ? 

Are investments professionals talking to eachothers about the stock pitches ? 

Isn't it sort of a given that if you have a good pitch you'll eventually come across someone who owns it? You wouldn't create a whole new pitch for each firm you talk to aside from a case study during a process, but that doesn't sound like what the question is about. If Firm A is your top choice you want to dedicate effort to, then yes maybe don't pick something they own. But if it is solid work you should be able to use it when talking to Firms B, C, and D and there is a chance someone might own it, especially if it is a good idea. 

You know in those singing shows like X-Factor, it's always not the best idea to sing the judge's own song

LOL. This is a terrible idea.