  We explore MHD solutions for envelope expansions with core collapse (EECC)
with isothermal MHD shocks in a quasi-spherical symmetry and outline potential
astrophysical applications of such magnetized shock flows. MHD shock solutions
are classified into three classes according to the downstream characteristics
near the core. Class I solutions are those characterized by free-fall collapses
towards the core downstream of an MHD shock, while Class II solutions are those
characterized by Larson-Penston (LP) type near the core downstream of an MHD
shock. Class III solutions are novel, sharing both features of Class I and II
solutions with the presence of a sufficiently strong magnetic field as a
prerequisite. Various MHD processes may occur within the regime of these
isothermal MHD shock similarity solutions, such as sub-magnetosonic
oscillations, free-fall core collapses, radial contractions and expansions. We
can also construct families of twin MHD shock solutions as well as an
`isothermal MHD shock' separating two magnetofluid regions of two different yet
constant temperatures. The versatile behaviours of such MHD shock solutions may
be utilized to model a wide range of astrophysical problems, including star
formation in magnetized molecular clouds, MHD link between the asymptotic giant
branch phase to the proto-planetary nebula phase with a hot central magnetized
white dwarf, relativistic MHD pulsar winds in supernova remnants, radio
afterglows of soft gamma-ray repeaters and so forth.
