Okay, so we know that in canon the young pre-hogwarts children are capable of doing magic when under duress and are also sometimes able to manage some early control (such as Lily in DH) but how far would these abilities go?
In PS Harry apparates onto the roof of his school and regrows his hair, and Lily in DH manages to control the growth of a flower. Ron mentions that the twins once turned his Teddy into a spider pre-Hogwarts. But how powerful/varied could a child's magic be?

(This initially occured to me because I was planning out at fic in which the younger sister of a Muggleborn student uses 'accidental' magic to apperate to help her sibling several miles away and I was worried it was implausible, but then I got to thinking about it more generally.