Young radio-loud active galactic nuclei form an important tool to investigate the evolution of extragalactic radio sources. To study the early phases of expanding radio sources, we have constructed CORALZ, a sample of 25 compact ($theta<2$) radio sources associated with nearby ($z<0.16$) galaxies. In this paper we determine the morphologies, linear sizes, and put first constraints on the lobe expansion speeds of the sources in the sample. We observed the radio sources from the CORALZ sample with MERLIN at 1.4 GHz or 1.6 GHz, the EVN at 1.6 GHz, and global VLBI at 1.6 GHz and/or 5.0 GHz. Radio maps, morphological classifications, and linear sizes are presented for all sources in the CORALZ sample. We have determined a first upper limit to the expansion velocity of one of the sources, which is remarkably low compared to the brighter GPS sources at higher redshifts, indicating a relation between radio luminosity and expansion speed, in agreement with analytical models. In addition we present further strong evidence that the spectral turnovers in GPS and CSS sources are caused by synchrotron self-absorption (SSA): the CORALZ sources are significantly offset from the well-known correlation between spectral peak frequency and angular size, but this correlation is recovered after correcting for the flux-density dependence, as predicted by SSA theory.
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