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We use Herschel 70 to 160um images to study the size of the far-infraredemitting region in about 400 local galaxies and quasar (QSO) hosts. The sampleincludes normal `main-sequence' star-forming galaxies, as well as infraredluminous galaxies and Palomar-Green QSOs, with different levels and structuresof star formation. Assuming Gaussian spatial distribution of the far-infrared(FIR) emission, the excellent stability of the Herschel point spread function(PSF) enables us to measure sizes well below the PSF width, by subtractingwidths in quadrature. We derive scalings of FIR size and surface brightness oflocal galaxies with FIR luminosity, with distance from the star-formingmain-sequence, and with FIR color. Luminosities L_FIR ~ 10^11 L_Sun can bereached with a variety of structures spanning 2 dex in size. UltraluminousL_FIR >~ 10^12 L_Sun galaxies far above the main-sequence inevitably have smallRe_70um ~ 0.5 kpc FIR emitting regions with large surface brightness, and canbe close to optically thick in the FIR on average over these regions. Comparedto these local relations, first ALMA sizes for the dust emission regions inhigh redshift galaxies, measured at somewhat longer rest wavelengths, suggestlarger sizes at the same IR luminosity. We report a remarkably tight relationwith 0.15 dex scatter between FIR surface brightness and the ratio of [CII]158um emission and FIR emission -- the so-called [CII]-deficit is more tightlylinked to surface brightness than to FIR luminosity or FIR color. Among 33 z <~0.1 PG QSOs with typical L_FIR/L_Bol,AGN ~ 0.1, 19 have a measured 70um halflight radius, with median Re_70um = 1.1kpc. This is consistent with the FIRsize for galaxies with similar L_FIR but lacking a QSO, in accordance with ascenario where the rest FIR emission of these types of QSOs is, in most cases,due to host star formation.

The far-infrared emitting region in local galaxies and QSOs: Size and scaling relations