Shortly after the discovery of fullerenes, many researchers pointed out that carbon nanotubes could be considered as elongated fullerenes. However, the detailed formation mechanism for both structures has been a topic of debate for several years, and consequently it has been difficult to draw a clear connection between the two systems. While the synthesis conditions appear to be different for both fullerenes and nanotubes, here, we demonstrate that it is highly likely that, at an initial growth stage, single-walled carbon nanotubes begin to grow from a hemisphere-like fullerene cap. More importantly, by analysing the minimum-energy path, it is shown that the insertion of C ₂ fragments drives the transformation of this fullerene cap into an elongated structure that leads to the formation of very short carbon nanotubes. This article is part of the themed issue ‘Fullerenes: past, present and future, celebrating the 30th anniversary of Buckminster Fullerene’.