I guess one major parameter will be how much the parent is present in kids life and whether they have good relationship. If the parent is not present, his or her impact will be smaller.

I agree with you, but GP was citing studies where the control variable you describe was adjusted and no effect measured.

Unfortunately, I have no idea which studies GP has in mind and what exactly they measured (whether things related to what I observed or something entirely else), age of kids in question, whether parents had significantly different approaches etc.

I don't think there is scientific a consensus on this yet. I strongly doubt that there is reasonable study that would make the split 50%, 50%, 0%. It is too round, too nice to be true.

Like I say, I agree with you in the broader sense but I was making a finer point here. i.e. not whether the premise is true, but just what the scope (or even how valid) was of the research that demonstrated the premise.

GP provides sources in a sibling thread where the discussion is further elaborated.

Ah, thanks. I did not seen sibling thread.