I base my definition loosely on distributed computing, where several computers are connected via a network to share aspects of tasks. It can be an entire virtual library, where the task of the librarians is to deliver information directly to desktops.
Distributed librarianship takes several forms.
It's the commercial bank that adds an information professional to the lending officer staff. It's the multinational that assigns librarians to specific projects and has them working with the project team to ensure that all information needs are not only met but anticipated. Getting librarians out to the individual business units is an aspect of distributed librarianship. Some librarians have been distributed to home offices, others to satellite offices within the company. One high-tech company has a division several states away from its headquarters.