This is something that everyone goes through. I still have problems with this . . . In fact, I would say that this is something that has negatively affected my career.
Employers read this "territorial" thing as an example of not playing with good team spirit. When I take on a new search assignment, for example, I am very territorial about the client and it's "MY project" (emphasis on the MY). That's a problem, because we have 17 global offices, and there are a lot of people who can help me. I have made great strides in improving this, but I know that my opportunities have been affected because I am not seen as the team player by some of my colleagues.
You've got to get past this. You've got to see the benefits that come to you by the synergy of working with others on your area of interest. Will you "lose" something in the process? Probably you will. But the overall gain will outweigh the loss of ownership you feel. Trust me -- it's a difficult lesson to learn,
“The world isn't fair, Calvin."
"I know Dad, but why isn't it ever unfair in my favor?”
― Bill Watterson, The Essential Calvin and Hobbes: A Calvin and Hobbes Treasury