Star-shaped mesogens with a phloroglucinol or a trimesic acid core and oligobenzoate arms with up to five repeating units have been synthesised. These non-conventional mesogens form various columnar mesophases over a broad temperature range. The liquid-crystal phases were characterised by optical microscopy, differential scanning calorimetry, X-ray diffraction, dilatometry and solid-state NMR spectroscopy. In addition to the high-temperature hexagonal columnar phases, the columnar self-assemblies undulate upon cooling and consequently form higher-ordered body-centred orthorhombic columnar 3D structures. A model of E-shaped folded conformers helically displaced along the columns is proposed. Helical preorganisation in the hexagonal phase precedes the transition to the low-temperature phases. Space filling and nano-segregation compete in the self-organisation process, thus aliphatic chains and the polar oligobenzoate scaffold are not perfectly separated in these star-shaped mesogens.