Context. Brightest cluster galaxies (BCGs) grow by accreting numerous smaller galaxies, and can be used as tracers of cluster formation and evolution in the cosmic web. However, there is still controversy regarding the main epoch of formation of BCGs; some authors believe they already formed before redshift z = 2, while others find that they are still evolving at more recent epochs. Aims. We study the physical properties of a large sample of BCGs covering a wide redshift range up to z = 1.8 and analyzed in a homogeneous way, to see if their characteristics vary with redshift. As a first step we also present a new tool to determine for each cluster which galaxy is the BCG. Methods. For a sample of 137 clusters with HST images in the optical and/or infrared, we analyzed the BCG properties by applying GALFIT with one or two Sérsic components. For each BCG we thus computed the Sérsic index, effective radius, major axis position angle, and surface brightness. We then searched for correlations of these quantities with redshift. Results. We find that the BCGs follow the Kormendy relation (between the effective radius and the mean surface brightness), with a slope that remains constant with redshift, but with a variation with redshift of the ordinate at the origin. Although the trends are faint, we find that the absolute magnitudes and the effective radii tend to become respectively brighter and bigger with decreasing redshift. On the other hand, we find no significant correlation of the mean surface brightnesses or Sérsic indices with redshift. The major axes of the cluster elongations and of the BCGs agree within 30° for 73% of our clusters at redshift z ≤ 0.9. Conclusions. Our results agree with the BCGs being mainly formed before redshift z = 2. The alignment of the major axes of BCGs with their clusters agree with the general idea that BCGs form at the same time as clusters by accreting matter along the filaments of the cosmic web.