1. Introduction

2. Data
2.1. Very Large Array 3 GHz radio continuum data

3. Analysis and results
3.1. Identification of the 3 GHz counterparts
3.2. Redshift distribution of the 3 GHz detected and non-detected submillimetre galaxies
3.3. Measurement of the size of the observed-frame 3 GHz radio emission
3.4. Spectral index between the observed frequencies of 1.4 GHz and 3 GHz, and 3 GHz brightness temperature

4. Discussion
4.1. Spectral indices and brightness temperatures
4.2. Comparison with other size measurements
4.3. Size evolution over cosmic time
4.4. Does the radio-emitting size depend on the galaxy morphology?
4.5. Potential biases in the radio size measurement, and the nature of submillimetre galaxies

5. Summary and conclusions