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GT-shadows are tantalizing objects that can be thought of as approximationsof elements of the mysterious Grothendieck-Teichmueller group $\widehat{GT}$introduced by V. Drinfeld in 1990. GT-shadows form a groupoid GTSh whoseobjects are finite index subgroups of the pure braid group PB_4, that arenormal in B_4. The goal of this paper is to describe the action of GT-shadowson Grothendieck's child's drawings and show that this action agrees with thatof $\widehat{GT}$. We discuss the hierarchy of orbits of child's drawings withrespect to the actions of GTSh, $\widehat{GT}$, and the absolute Galois groupG_Q of rationals. We prove that the monodromy group and the passport of achild's drawing are invariant with respect to the action of the subgroupoid ofcharming GT-shadows. We use the action of GT-shadows on child's drawings toprove that every Abelian child's drawing admits a Belyi pair defined overrationals. Finally, we describe selected examples of non-Abelian child'sdrawings.

The Action of GT-Shadows on Child's Drawings