The imprints of dust-starlight interactions are visible in scaling relations between stellar characteristics, star formation parameters and dust properties. We aim to examine dust scaling relations on a sub-kpc resolution in the Andromeda galaxy (M31) by comparing the properties on a local and global scale to other galaxies of the local universe. New Herschel observations are combined with available data from GALEX, SDSS, WISE and Spitzer to construct a dataset covering UV to submm wavelengths. We work at the resolution of the SPIRE $500; mu$m beam, with pixels corresponding to physical regions of 137 x 608 pc in the galaxys disk. A panchromatic spectral energy distribution was modelled for each pixel and several dust scaling relations are investigated. We find, on a sub-kpc scale, strong correlations between $M_d/M_star$ and NUV-r, and between $M_d/M_star$ and $mu_star$ (the stellar mass surface density). Striking similarities with corresponding relations based on integrated galaxies are found. We decompose M31 in four macro-regions based on their FIR morphology; the bulge, inner disk, star forming ring and the outer disk. All regions closely follow the galaxy-scale average trends. The specific star formation characteristics we derive for these macro-regions give strong hints of an inside-out formation of the bulge-disk geometry, as well as an internal downsizing process. However, within each macro-region, a great diversity in individual micro-regions is found. Furthermore, we confirm that dust in the bulge of M31 is heated only by the old stellar populations. In general, the local dust scaling relations indicate that the dust content in M31 is maintained by a subtle interplay of past and present star formation. The similarity with galaxy-based relations strongly suggests that they are in situ correlations, with underlying processes that must be local in nature. (Abriged)
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