In Leila Schneps, editor, *The Grothendieck theory of
Dessins d'Enfants*, number 200 in Lecture Notes in Math., pages 79--113.
Cambridge University Press, 1994.
**Abstract:**
We study the topological aspects of dessins (via analytic
description) with two distinct goals. Firstly we are interested in fields of
definition and fields of moduli. We give a topological proof that there exist
some dessins with no model defined over their field of moduli. This answers
explicitly a question asked in Harbater. Our second motivation is to collect
practical and theoretical data for the explicit computation of covers given
by some topological description, following ideas of Atkin, Oesterle and
ourselves. This leads to a method for the computation of the linear space
associated to a divisor on a given dessin.