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The EUV line emission and relative line-of-sight velocity in the transition region between the chromosphere and corona of 36 sunspot regions are investigated, based on observations with the Coronal Diagnostic Spectrometer - CDS and the Solar Ultraviolet Measurements of Emitted Radiation - SUMER on the Solar and Heliospheric Observatory - SOHO. The most prominent features in the transition-region intensity maps are the sunspot plumes. In the temperature range between log T=5.2 and log T=5.6 we find that 29 of the 36 sunspots contain one or two sunspot plumes. The relative line-of-sight velocity in sunspot plumes is high and directed into the Sun in the transition region, for 19 of the sunspots the maximum velocity exceeds 25 km s^sup -1^. The velocity increases with increasing temperature, reaches a maximum close to log T=5.5 and then decreases abruptly. Attention is given to the properties of oscillations with a period of 3 min in the sunspot transition region, based on observations of six sunspots. Comparing loci with the same phase we find that the 3-min oscillations affect the entire umbral transition region and part of the penumbral transition region. Above the umbra the observed relation between the oscillations in peak line intensity and line-of-sight velocity is compatible with the hypothesis that the oscillations are caused by upward-propagating acoustic waves. Information about intensity oscillations in the low corona is obtained from observations of one sunspot in the 171 Å channel with the Transition Region And Coronal Explorer - TRACE. We conclude that we observe the 3-min sunspot oscillations in the chromosphere, the transition region and the low corona. The oscillations are observable over a wider temperature range than the sunspot plumes, and show a different spatial distribution than that of the plumes.[PUBLICATION ABSTRACT]