Recent works by Boston, Wood, and others suggest a balanced presentation random model for 'nonabelian class groups'. We show that over function fields, these class groups (etale fundamental groups) are indeed balanced.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/9073