1. to delegate a task assigned to you, back to the person who assigned it.
2. to delegate a task assigned to you, over to someone else, usually a co-worker.
Basically, to deflect and redirect responsibility for a task or job.
Derived from the words 'boomerang' and 'delegate'. Can also be used as a noun, see example 3.
2. The boss delegated me with this task, which I am now boomegating over to you...
3. "Tossing to you... you can deflect to him but my boomegate blocker is up."