Two types of complex nanotubes produced by the are-discharge method are investigated in this study: multi-walled carbon nanotubes filled with metallic nanowires and composite BN-C nanotubes. Their multi-element character yields specific spatial chemical arrangements - deduced from transmission electron microscopy (TEM) studies - which give precious information about the growth mechanism of nanotubes. Concerning filled nanotubes, if the metal-graphite cathode is carbon free, no filling is obtained, whereas if it contains sulfur - either as an impurity of graphite or when added under controlled quantities - complete or very long fillings are achieved, even for metals with very high melting temperatures. The chemical analyses revealed various types of fillings: pure sulfides, grains of sulfides alternating with grains of pure metals, or in some specific cases, pure metals. As for the B-C-N tubes, a total phase separation is observed between BN and C, and these two phases form concentric shells typically of the C/BN/C type. In this paper, we show that an approach combining the vapor-liquid-solid (VLS) scheme and the characteristics of the solidification given by phase diagrams account very well for the observed structures. The contrast between the absence of filling, when a sulfur-free carbon-metal rod is used for the cathode, and the successful fillings, when sulfur is added, is explained by metal-sulfur phase diagrams: adding sulfur to a liquid metal decreases the solidification temperature. The different types of fillings are also explained by the nature of the sulfur-metal phase diagram. An eutectic solidification, such as in Ni-S, yields two phases - the pure metal and the first sulfide - within a given tube, whereas the existence of a miscibility gap in the liquid, such as in Cr-S, leads to two separate liquids and, therefore, to two different fillings. In the same way, the eutectic-like pseudo-binary C-BN phase diagram explains not only the complete phase separation between BN and C, but also the observed organisation between layers: we propose that the latter is due to a sequential solidification of the two phases. As a perspective, this phase diagram approach is also discussed in the context of the formation of ropes of single-walled carbon nanotubes from the solidification of a metal-carbon liquid particle.