  We determine the radio size distribution of a large sample of 152 SMGs in
COSMOS that were detected with ALMA at 1.3 mm. For this purpose, we used the
observations taken by the VLA-COSMOS 3 GHz Large Project. One hundred and
fifteen of the 152 target SMGs were found to have a 3 GHz counterpart. The
median value of the major axis FWHM at 3 GHz is derived to be $4.6\pm0.4$ kpc.
The radio sizes show no evolutionary trend with redshift, or difference between
different galaxy morphologies. We also derived the spectral indices between 1.4
and 3 GHz, and 3 GHz brightness temperatures for the sources, and the median
values were found to be $\alpha=-0.67$ and $T_{\rm B}=12.6\pm2$ K. Three of the
target SMGs, which are also detected with the VLBA, show clearly higher
brightness temperatures than the typical values. Although the observed radio
emission appears to be predominantly powered by star formation and supernova
activity, our results provide a strong indication of the presence of an AGN in
the VLBA and X-ray-detected SMG AzTEC/C61. The median radio-emitting size we
have derived is 1.5-3 times larger than the typical FIR dust-emitting sizes of
SMGs, but similar to that of the SMGs' molecular gas component traced through
mid-$J$ line emission of CO. The physical conditions of SMGs probably render
the diffusion of cosmic-ray electrons inefficient, and hence an unlikely
process to lead to the observed extended radio sizes. Instead, our results
point towards a scenario where SMGs are driven by galaxy interactions and
mergers. Besides triggering vigorous starbursts, galaxy collisions can also
pull out the magnetised fluids from the interacting disks, and give rise to a
taffy-like synchrotron-emitting bridge. This provides an explanation for the
spatially extended radio emission of SMGs, and can also cause a deviation from
the well-known IR-radio correlation.
