The recently synthesized cyclo[18]carbon molecule has been characterized in a number of studies by calculating electronic, spectroscopic, and mechanical properties. However, cyclo[18]carbon is only one member of the class of cyclo[n]carbons-standalone carbon allotrope representatives. Many of the larger members of this class of molecules have not been thoroughly investigated. In this work, we calculate the magnetically induced current density of cyclo[n]carbons in order to elucidate how electron delocalization and aromatic properties change with the size of the molecular ring (n), where n is an even number between 6 and 100. We find that the Hückel rules for aromaticity (4k + 2) and antiaromaticity (4k) become degenerate for large Cn rings (n > 50), which can be understood as a transition from a delocalized electronic structure to a nonaromatic structure with localized current density fluxes in the triple bonds. Actually, the calculations suggest that cyclo[n]carbons with n > 50 are nonaromatic cyclic polyalkynes. The influence of the amount of nonlocal exchange and the asymptotic behavior of the exchange-correlation potential of the employed density functionals on the strength of the magnetically induced ring current and the aromatic character of the large cyclo[n]carbons is also discussed.