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

Classification of three-family flavoured DFSZ axion models that have no domain wall problem