There are several ways associates can leverage the experience, reputation, work load and knowledge of senior partners. The first thing to mention is that you have to be proactive. Don’t wait for them to come to you-they have their own practice and life to worry about and are not likely sitting at their desk thinking of ways to help you. So if it’s work you are after, make a point of walking the halls everyday and popping into their offices to see what they are working on. I have heard that if you bug them enough they will throw you a file just to get rid of you.
If you are looking to raise your profile and don’t think you have enough experience to write an article, approach a partner to co-write it with you. (Meaning you do all the work and they edit it and add their name to it along side yours). You still get the name recognition and profile raising as well as experience getting published.
If you don’t have a mentor or you don’t get along well with your assigned mentor, look for someone who you would work better with and make the request. This is your career. Be more proactive in getting what you want.