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In Part I we gave a polynomial growth lower-bound for the number of nodaldomains of a Hecke-Maass cuspform in a compact part of the modular surface,assuming a Lindel\"of hypothesis. That was a consequence of a topologicalargument and known subconvexity estimates, together with new sharp lower-boundrestriction theorems for the Maass forms. This paper deals with the samequestion for general (compact or not) arithmetic surfaces which have areflective symmetry. The topological argument is extended and representationtheoretic methods are needed for the restriction theorems, together withresults of Waldspurger. Various explicit examples are given and studied.

Nodal domains of Maass forms II