I'm currently finishing the corrections of the PhD I've done in the UK. In the meantime, I've returned to my home country, Portugal, and started working at a hospital as a medical statistician. I have several (no scientific tasks) to do and I would like to continue doing research. I have several projects that I would like to carry one. Some are not very complicated and I believe they could be interesting master degree thesis. While in the UK, I've supervised some undergrads and I really enjoyed. I would like to continue supervising students.
Does anyone have any experience or guidance about how could I start to supervise research students (proposing small projects)? I don't need to be affiliated with a university to be a supervisor as my master thesis supervisor was not a teacher there. But, do I need to be affiliated with a university to propose projects? I imagine I can only be a supervisor in Portugal or has anyone heard about master degree supervisors from other countries? I understand this may differ between countries. I'm looking for some tips/advice/comments on how to start supervising students.