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We present deep, high‐quality  K ‐band images of complete subsamples of powerful radio and submillimetre galaxies at redshifts   z ≃ 2 . The data were obtained in the very best available seeing via queue‐based observations at the United Kingdom Infrared Telescope and Gemini‐North, with integration times scaled to ensure that comparable rest‐frame surface brightness levels are reached for all of the galaxies. We fit two‐dimensional axisymmetric galaxy models to these images to determine basic galaxy morphological parameters at rest‐frame optical wavelengths  λ rest  &gt; 4000  Å, varying luminosity, axial ratio, half‐light radius   r  1/2   and Sérsic index  n . We find that, while a minority of the images show some evidence of galaxy interactions, &gt;95 per cent of the rest‐frame optical light in all the galaxies is well described by these simple axisymmetric models. We also find evidence for a clear difference in morphology between these two classes of galaxy; fits to the individual images and to the image stacks reveal that the radio galaxies are moderately large ( 〈 r  1/2 〉= 8.4 ± 1.1 kpc ; median   r  1/2 = 7.8 ) de Vaucouleurs spheroids ( 〈 n 〉= 4.07 ± 0.27 ; median   n = 3.87 ), while the submillimetre galaxies appear to be moderately compact ( 〈 r  1/2 〉= 3.4 ± 0.3 kpc ; median   r  1/2 = 3.1 kpc ) exponential discs ( 〈 n 〉= 1.44 ± 0.16 ; median   n = 1.08 ). Model fits to the stacked images yield very similar results. We show that the   z ≃ 2  radio galaxies display a well‐defined Kormendy ( μ  e  – r e   ) relation but that, while larger than other recently studied massive galaxy populations at comparable redshifts, they are still a factor of  ≃1.5  times smaller than their local counterparts. The scalelengths of the starlight in the submillimetre galaxies are comparable to those reported for the molecular gas, suggesting that the two may be colocated. Their sizes are also similar to those of comparably massive quiescent galaxies at   z  &gt; 1.5 , allowing the possibility of an evolutionary connection following cessation/quenching of the observed star formation activity. In terms of stellar mass surface density, the majority of the radio galaxies lie within the locus defined by local ellipticals of comparable stellar mass. In contrast, while best modelled as discs at the epoch of bright dust‐enshrouded star formation, most of the submillimetre galaxies have higher stellar mass densities than local galaxies, and appear destined to evolve into present‐day massive ellipticals.

A near‐infrared morphological comparison of high‐redshift submillimetre and radio galaxies: massive star‐forming discs versus relaxed spheroids