  We provide an exhaustive classification of three-family DFSZ axion models
that have no cosmological domain wall problem. This result is obtained by
making the Peccei-Quinn symmetry flavour dependent in certain specific ways,
thus reinforcing a possible connection between the strong CP problem and the
flavour puzzle. Known DFSZ flavour variants such as the top-specific model
emerge as special cases. Key features of the phenomenology of these models are
briefly discussed.
