We systematically investigated the principles of actin cytoskeleton self-organization in two cell types, fibroblasts and epitheliocytes, by confining isolated cells on isotropic adhesive islands of varying size. In fibroblasts, we previously described that an initially circular pattern of circumferential actin dynamically evolves into a radial pattern of actin bundles that spontaneously transforms into a chiral pattern, before finally producing parallel linear stress fibres. We now show that progression from circular to chiral actin patterns depends on cell projected area and rarely occurs on small islands. Epitheliocytes however, did not exhibit succession through all the actin patterns described above even on large islands. Upon confinement, the actin cytoskeleton in non-keratinocyte epitheliocytes is arrested at the circular stage, while in keratinocytes it can progress as far as the radial pattern but still cannot break symmetry. Epithelial-mesenchymal transition pushed actin cytoskeleton development from circular towards radial patterns but remains insufficient to cause chirality. Surprisingly, small doses of G-actin sequestering drug, latrunculin A, induced chiral swirling in keratinocytes. During this swirling, keratin filaments follow actin and also demonstrate chiral swirling movement. Elimination of the keratin network by genetic silencing of Type II keratins, however, did not affect the self-organization of the actin cytoskeleton.