Star Pupil's ability doesn't cause you to move counters from itself to the target creature. Rather, you put the same number of each kind of counter Star Pupil had when it died onto that creature.

If Star Pupil has -1/-1 counters on it when it dies, the last ability will include those as well. This may result in the recipient also dying.

Star Pupil puts all of its counters onto the target creature, not just its +1/+1 counters.

In some unusual cases, you may end up putting the appropriate counters on more than one permanent. For example, if you control The Ozolith when Star Pupil dies, you will put the appropriate number of each kind of counter onto both The Ozolith and the target creature.