I see an apprentice/mentor relationship as primarily the apprentice working on the mentor's project/work. In any case the mentor and apprentice have to discuss who each of them expect since no one wants to give out valuable model files and resources to a stranger and then have them quit a few days in because they don't like being stuck with tweening duties for the first few weeks.
This relationship requires dedication on both halves to complete what ever projects that are going on.
Some things to consider in order for this to work.
The apprentice has to tell the mentor how much time they have available and what skills they have (samples would help here). Time is really important as it will determine if the apprentice is given too little to do or gets overwhelmed. The apprentice will need to be very clear about how much time they will actually spend on a project. I may have 3 hrs a night free but reality is that i spend an hour winding down from work or playing a game and another hour working on my own stuff so I really have an hour free for my potential mentor. There is a big difference between 5 hours a week and 15 and the difference can spell dissater for a mentor who uses an apprentice on a paying job.
The mentor has to discuss what the apprentice will be required to do and how they will go about sharing files and resources. Also the mentor has to make clear what they can teach. If the mentor is a great animator and a bad texture artist then an apprentice who is looking to improve their texturing will have wasted both his and the mentor's time.
That brings up another point. Trading skills might be a cool thing too, an animator may teach the texture artist his skills in return for learning how to texture.
people who want to apprentice have to realize that they are not only learning how to animate/model but may have access to models, cho, actions and other material they would never have access to otherwise. Think of it like a class but with a private tutor you don't have to pay.