  In the context of the 2HDM, and assuming that neutrinos acquire masses via
the Weinberg operator, we perform a systematic analysis to determine the
minimal quark and lepton flavour patterns, compatible with masses, mixing and
CP violation data, realisable by Abelian symmetries. We determine four minimal
models for quarks, where the number of independent parameters matches the
number of observables. For the lepton sector, three minimal predictive models
are identified. Namely, we find scenarios with a preference for the upper/lower
octant of the $\theta_{23}$ atmospheric mixing angle, that exhibit lower bounds
on the lightest neutrino masses currently probed by cosmology and testable at
future neutrinoless double beta decay experiments, even for a normally-ordered
neutrino masses. We investigate the phenomenology of each model taking into
account all relevant theoretical, electroweak precision observables, scalar
sector constraints, as well as stringent quark flavour processes such as
$\overline{B} \rightarrow X_s \gamma$, $B_s \rightarrow \mu^- \mu^+$ and meson
oscillations, and the charged lepton flavour-violating decays $e_\alpha^{-}
\rightarrow e_\beta^{-} e_\gamma^{+} e_\delta^{-}$ and $e_\alpha \rightarrow
e_\beta \gamma$. We show that, in some cases, Abelian flavour symmetries
provide a natural framework to suppress flavour-changing neutral couplings and
lead to scenarios featuring heavy neutral/charged scalar masses below the TeV
scale within the reach of current experiments.
