Extremely short (<1 nm) fragments of zig-zag carbon nanotubes are studied with ab-initio techniques to determine their geometric and electronic structure as well as their magnetic susceptibility. It is found that for lengths of a few carbon–carbon bonds, each fragment can be viewed as composed of crowns, that is, zig-zag rings of carbon atoms along the circumference of the tube. In this case, two kinds of electronic structures are found, depending on whether the number of carbon atoms in each crown is even or odd. Systems comprising three or more crowns either have a high spin ground state or involve a charge transfer across the length of the fragment. Conjugation changes qualitatively when the length of the fragment approaches and surpasses its girth. Indications regarding the predicted chemical stability and electronic response are provided and interpreted in terms of current densities induced within each crown by a magnetic field along the tube axis.