Freestanding, vertical, multiwalled carbon nanotubes (MWCNTs) are formed during the vacuum deposition of thin films of the metastable carbides CT3 (T=Ni, Co) onto fire-polished glass substrates. In contrast to widely used chemical and laser vapor deposition techniques, we utilize direct e-beam evaporation of arc-melted CT3 targets to produce MWCNTs that are self-assembled out of the CT3-film matrix. The depositions are made in an ambient vapor pressure that is at least six orders of magnitude lower than the 1-100 Torr typically used in chemical vapor techniques. Furthermore, the substrates need not be heated, and, in fact, we observe a robust nanotube growth on liquid nitrogen cooled glass and sapphire substrates. High-resolution atomic force microscopy reveals that MWCNTs of heights 1-40 nm are formed in films with nominal thicknesses in the range of 5-60 nm. We show that the growth parameters of the nanotubes are very sensitive to the grain structure of the films. This is consistent with a precipitation mediated root-growth mechanism.