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See:
http://stackoverflow.com/questions/30943161/multiprocessing-pool-with-maxtasksperchild-produces-equal-pids
The documentation never makes clear what a "task" in the context of Pool.map. At best, it says:
"This method chops the iterable into a number of chunks which it submits to the process pool as separate tasks. The (approximate) size of these chunks can be specified by setting chunksize to a positive integer."
in the map documentation. However it does not say how this chunks are calculated by default, making the maxtasksperchild argument not very useful. The fact that a function evaluated by map is not a "task" should be much clearer in the documentation.
Also, in the examples, such as:
 with multiprocessing.Pool(PROCESSES) as pool:
 #
 # Tests
 #
 TASKS = [(mul, (i, 7)) for i in range(10)] + \
 [(plus, (i, 8)) for i in range(10)]
 results = [pool.apply_async(calculate, t) for t in TASKS]
 imap_it = pool.imap(calculatestar, TASKS)
 imap_unordered_it = pool.imap_unordered(calculatestar, TASKS)
TASKS are not actually "tasks" but rather "task groups".

I second this. I was definitely confused at first and it took me a little while of googling to realize that jobs are not what one (at least me) would intuitively think they are.