  We study the distribution and scaling of the extreme height fluctuations for
Edwards-Wilkinson-type relaxation on small-world substrates. When random links
are added to a one-dimensional lattice, the average size of the fluctuations
becomes finite (synchronized state) and the extreme height diverges only
logarithmically in the large system-size limit. This latter property ensures
synchronization in a practical sense in small-world coupled multi-component
autonomous systems. The statistics of the extreme heights is governed by the
Fisher-Tippett-Gumbel distribution.
