Given the topic's importance, Halliburton's essay should be better. He rightly stresses the centrality of anointing both to the early baptismal rites and to their interpretations, but his description is synthetic and shallow. Water was linked to death and resurrection, making the new person, while oil was a seal against demons, preparing one for the virtuous life. Brock and Hall deal with a single tradition each, Syriac and Byzantine. Brock's essay is as satisfying as one would expect.
All anointing is grounded in baptism, even anointing the sick and penitent.
Anointing the sick was long informal, with Eastern rites coalescing around the twelfth century. The Byzantine rites, unwieldy and repetitious, may reflect a combining of rites, as Grisbrooke notes. One wonders if the formal rites were ever common and if simpler practices continued popularly. Returning to earlier chapters, Bowie provides a suggestive collection of observations on the classical through early imperial periods. Roman moralists frowned on unguent as a Greek luxury, but Latin practices generally matched Greek ones.