To claim or seize without justification.
Example:
With this legislation, Governor Burns insisted, the federal government was trying to arrogate powers previously held by the states.
A project team will probably succeed best if individual members do not try to arrogate decision-making authority to themselves. And many of us are annoyed when television evangelists try to arrogate to themselves the right to decide what kind of faith is acceptable. (Because of their similarity, it is all to easy to confuse arrogate with abrogate -- and with arrogant, for that matter. Study them carefully.)