I have owned several parakeet when I was a kid. None of them was that attached to me. Well if they were really attached then they wouldn't disappear after they broken the cage. From some youtube videos I have seen, these birds can be cage free at home. That will require some serious "attachment".
I also read somewhere said that if you get a single bird, it is easier to have the bird attached to you, because if you have two birds they will more likely be attached to each other. Is it true?
How did you make your birds become attached to you?
How old was the bird when first arrived?
How long did it take?