I'm a very hands-off manager. Do the management books have a name for that? Don't get me wrong - I'm very available to my co-workers. "My door is always open" and all that (although, more sincerely than that old cliche sounds. It really, literally, is open!), but I trust each of them implicitly. While I'm aware of what they're working on and how it's going, I do not micro-manage or get in their way. I can't stand the thought of nit-picking every little thing or being in their way all the time. They are professionals and they will come to me for a) time, b) resources, or c) advice as needed...and they do.
I was "raised" as a professional librarian by directors who were aware and available, but not micro-managers, so I have followed that model. Hands-off doesn't mean I'm not willing to be hands-on; it means I wait to be invited to the party and leave my involvement at "aware overseer" otherwise. My job is to give my co-workers the time, resources, and support they need to do their jobs.
I love hands-on library work, but I never impose myself on the others' projects. They're fine, and they will ask for help when they need it (at which time I will jump at the chance to play whenever possible!) One of my responsibilities is to provide learning opportunities for the Interns and to keep the Reference Assistants engaged, interested, and invested in their jobs. That means that most often when hands-on help is asked for by the librarians, I have to pass it on to an Intern or RA, rather than do it myself (no matter how much I'd like to!). There just aren't enough cool projects to share with them to go around, so they get most of them. I jump in where go-between is necessary between upper management and other staff, or where a decision has to be made before work can continue. I listen to concerns and ideas and then provide the resources to make things happen. I set up the meeting. I re-arrange the budget. I get buy-in from the staff. I evaluate how it worked.
Here's the other management philosophy I believe strongly: don't expect your co-workers to do anything you aren't willing to do. I'm willing to handle rowdy teens, deal with stinky and belligerent patrons, take extra service desk time, cleaning/plumbing/fixing, and anything else that may come up. I will never ask anyone else to do something just because I don't feel like it or because it's uncomfortable. I may ask them because I'm not available, but never because I'm not willing.
So, my management style is intended to be hands-off but ready to be hands-on at a moment's notice, always willing, usually able, always approachable, usually flexible, and always, always, always as an active part of the team.