Belyi's theorem states that every smooth projective algebraic curve $C$ defined over $\bar{\mathbb{Q}}$
admits a map $C\to\mathbb{P}^1$ ramified only over $0,1,\infty$.
Is there an analogue of this theorem with $\mathbb{Q}$ replaced by a global function field (i.e. finite extension $\mathbb{F}\_q(t)$)?


I am especially interested in the existence of a tamely ramified map.



Belyi's theorem for function fields
Much stronger results are available in positive characteristic. See 


Kedlaya, Kiran S.


More étale covers of affine spaces in positive characteristic.
J. Algebraic Geom. 14 (2005), no. 1, 187–192. 


