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For many years proto-planetary discs have been thought to evolve viscously:angular momentum redistribution leads to accretion and outward disc spreading.Recently, the hypothesis that accretion is due, instead, to angular momentumremoval by magnetic winds gained new popularity: no disc spreading is expectedin this case. In this paper, we run several one-dimensional gas and dustsimulations to make predictions on the time-evolution of disc sizes \textit{inthe dust} and to assess whether they can be used to understand how discsevolve. We show that viscous and magnetic wind models have very different dustdisc radii. In particular, MHD wind models are compact and their sizes eitherremain constant or decrease with time. On the contrary, discs become largerwith time in the viscous case (when $\alpha\gtrsim10^{-3}$). Although currentobservations lack enough sensitivity to discriminate between these twoscenarios, higher-sensitivity surveys could be fruitful to this goal on a$1\,{\rm to}\,10\,{\rm Myr}$ age range. When compared with the available ALMABand~7 data, both viscous and magnetic wind models are compatible with theobservationally-inferred dust radii in Lupus, Chamaeleon~I and Upper Sco.Furthermore, in the drift-dominated regime, the size-luminosity correlation isreproduced in Lupus, both in Band~7 and 3, while in Upper Sco a different slopethan in the data is predicted. Sub-structures (potentially undetected) canexplain several outliers with large observed sizes. Higher-angular-resolutionobservations will be helpful to test our predictions in the case of morecompact discs, expected in both frameworks, particularly at the age of UpperSco.

Modelling the secular evolution of proto-planetary disc dust sizes -- A comparison between the viscous and magnetic wind case