I've seen many times that the most important thing to look for is how famous/important/havealotofpublications is the supervisor. Is this a rule?. I can easily see supervisors getting papers published all the time and not caring at all for the students... Is not more important the program you do?

The reason we emphasise the importance of the supervisor is to show people to look deeper than just the reputation of the university. A less well known university can still employ people who are world leaders in their field. Your point about high profile supervisors who ignore their students is a good one. We advise anyone going for interview to talk to other members of the lab they hope to join to see what they think of the supervision. You should also never accept a project you're not interested in just because the supervisor's got a good reputation. A point which we haven't mentioned before is that a supervisor at the start of their career will have a smaller research group and can be a very good choice as they have less demands on their time and will probably still be doing their own lab work. If you are somebody's first student you will be very important to them.