For one, I think that mentors should be chosen by the mentee based on the unique skills/experience they possess that the mentee hopes to acquire/learn. What use can come of a mentor randomly assigned by some system? Also, in my experience both as a mentor and a mentee long-distance relationships fizzle out too quickly and don't amount to much. If you want to have a truly worthwhile mentorship experience, I would suggest approaching a person you would really like to be your mentor and just asking if you could meet for coffee/lunch/walk in the park/whatever once a month or so.
And I will use this opportunity to give an anonymous shout-out of appreciation to several professors I had, both in undergrad and in pharmacy school, who were my mentors, though I did not understand or appreciate it at the time. It was just so intuitive to go up to their office and ask if I could come in because I had a quick question, not about class, but about profession/life in general. And then leave two hours later, having talked about everything under the sun.
