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The last example which illustrates my point quite well.

How would you say?

1) Я заставил своего ребёнка ждать меня возле школы.
2) Я заставил своего ребёнка ждать себя возле школы.

I would...

As long as we have only two persons in our sentence any ambiguity is ruled out. You are correct that that somebody isn't mentioned, hence, it would be incorrect to refer to someone who hasn't been...

Well, I am not a great expert of Russian (even though it's my first language), but I doubt that it's perfectly correct in this context, at least. I think "его" is the better alternative. Why? Because...

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With all due respect to iCake's Russian version, I think that the usage of себя is not correct here. To me it means that the child was made to wait for himself,...