  We present a theory of 'maximal' super-KP(SKP) hierarchy whose flows are
maximally extended to include all those of known SKP hierarchies, including,
for example, the MRSKP hierarchy of Manin and Radul and the Jacobian SKP(JSKP)
introduced by Mulase and Rabin. It is shown that SKP hierarchies has a natural
field theoretic description in terms of the B-C system, in analogous way as the
ordinary KP hierarchy. For this SKP hierarchy, we construct the vertex
operators by using Kac-van de Leur superbosonization. The vertex operators act
on the \(\tau\)-function and then produce the wave function and the dual wave
function of the hierarchy. Thereby we achieve the description of the 'maximal'
SKP hierarchy in terms of the \(\tau\)-function, which seemed to be lacking
till now. Mutual relations among the SKP hierarchies are clarified. The MRSKP
and the JSKP hierarchies are obtained as special cases when the time variables
are appropriately restricted.
