External co-supervision of a thesis or publication involves collaborating with an individual not affiliated with the primary institution or research group. While specific rules and rights may vary depending on the institution and field of study, I can provide a general outline of standard practices and considerations. Here are some key points to keep in mind:

1. Consent and Agreement: The leading professor or advisor should be informed and provide consent for external co-supervision. It is essential to obtain their approval before involving an external co-supervisor.

2. Selection of External Co-Supervisor: The external co-supervisor should possess relevant expertise and qualifications in the field of study. The selection process typically involves evaluating their academic credentials, research experience, and professional reputation.

3. Responsibilities and Contributions: The roles and responsibilities of the external co-supervisor should be clearly defined and agreed upon by all parties involved. This may include providing guidance, reviewing drafts, offering feedback, and participating in research discussions. The extent of their involvement may vary depending on the specific project and the agreement made.

4. Data Protection: Protecting research data is crucial. All parties involved must adhere to ethical guidelines and data protection regulations. Measures should be implemented to maintain the data's confidentiality, integrity, and security throughout the collaboration.

5. Intellectual Property Rights: Rights can vary depending on institutional policies, funding sources, and legal frameworks. Establishing an explicit agreement regarding the ownership and use of intellectual property generated during the collaboration is essential. This may include guidelines for patents, copyrights, and publications.

6. Authorship and Publication: The external co-supervisor's contribution should be appropriately recognized. In cases where the co-supervisor has made significant intellectual contributions to the research, they may be listed as a co-author in related publications. The authorship order should be determined based on established conventions in the field and each author's contribution.

7. Conflict Resolution: It is important to establish mechanisms for conflict resolution and dispute management in case any disagreements arise during the collaboration. This can help ensure a smooth working relationship and prevent potential issues from escalating.

It is essential to consult the specific guidelines and policies of your institution or research group for a more detailed understanding of the rules and rights related to external co-supervision.