Advisor's/University's rights in the PhD/MSc alumni's research projects and publications After a series of discussions about the level of dependency of a research student on his advisor in this link and this link, a question comes to mind that when the person is graduated and leaves the university; even he is now working independently in a company or he is a faculty member of a university; as far as most of the researches he is going to do may be based on his PhD dissertation;  


Until when should this person contact his supervisor about the researches he is doing?  
Should he ethically acknowledge that his researches is roots of his PhD project under his advisor's supervision?  
If, based on his dissertation, he works on a research project; should he talk about it to his supervisor and he should be aware on every single after-PhD project? Just because the base of the publication and research is the PhD dissertation which is done under his supervision?  
To put in a nutshell, as a matter of academic ethics, what are exact rights of a supervisor in projects done based on his student's supervision (after graduation of the person)? What are the rights of the university from which the student is graduated?
I am currently returning now to a thread of work that I started as a PhD student many years ago, but have not had opportunity to work on since then. I will not be including my advisors as authors on the new papers that result, because the work goes beyond anything that we worked on or discussed during that project. So there's no direct overlap there, and thus they have no intellectual investment in the project.

I would argue that you would continue to include the advisors if they are actively collaborating with you on the current work that you're publishing—or if the original work that you're publishing was done while you were under their supervision. 

Of course, you do need to cite the previous work that you've done on the topic as part of placing the work in its appropriate context within the larger experience. You should also be notifying your advisors of your recent work because it's the smart thing to do—you should always keep mentors apprised of your ongoing research activities!