The "doping" of carbon nanotubes with heteroatoms is an established method of controlling their properties. However, variations in heteroatom concentration in multiwalled carbon nanotubes (MWCNTs) tend to produce nanotubes with different morphologies, and hence varying properties, within the same sample. Electron energy loss spectroscopy in conjunction with imaging using a scanning transmission electron microscope (STEM) is a powerful tool to precisely map the spatial variation and bonding state of heteroatoms, e.g., B, N, P, Si, or combinations of these, present in carbon nanotubes exhibiting different structures. TEM analysis revealed that B incorporation during MWCNT growth (B-MWCNTs) results in nanotube morphologies that can be divided into three different types. These include core-shell structures possessing a B-rich core of cones and a C outer layer, B-containing cone structures, and MWCNTs with an irregular inner channel. In situ studies were carried out using Nanofactory() holder experiments in order to investigate the properties of individual B-MWCNTs and to show that the three types of nanotubes undergo different current-induced breakdown. The inhomogeneity in composition, structure, and properties of B-MWCNTs could result from the variation in chemical composition and temperature within the furnace, and this work highlights the importance of developing synthesis techniques that can control the inclusion of heteroatoms into nanotubes.