My kid "drew or wrote messily" on the paper (look at the picture)
all over the place (British English also all over the shop) (US English also all over the lot) (informal)
1-everywhere
New restaurants are appearing all over the place.
2-not neat or tidy; not well organized
Your calculations are all over the place (= completely wrong).
I am thinking about "to write or draw all over the place", but not sure if it is idiomatic.