  Extension procedure for supermanifold ${\cal M}_{cl}$ of superfields ${\cal
A}^{\imath}(\theta)$, ghost number construction are considered. Classical and
$\hbar$-deformed generating (master) equations, existence theorems for their
solutions are formulated in $T^{\ast}_{odd}{\cal M}_{min}$,
$T^{\ast}_{odd}{\cal M}_{ext}$. Analogous scheme is realized for BV similar
generating equations. Master equations versions for GSQM and BV similar scheme
are deformed in powers of superfields ${\stackrel{\circ}{\Gamma}}{}^p(\theta)$
= $\bigl({\stackrel{\circ}{\Phi}}{}^B(\theta)$,
${\stackrel{\circ}{\Phi}}{}^{\ast}_B(\theta)\bigr)$ into supermanifold
$T_{odd}(T^{\ast}_{odd}{\cal M}_{ext})$. Arbitrariness in a choice of solutions
for these equations is described. Investigation of formal Hamiltonian systems
for II class theories [2] defined via corresponding master equations solutions
is conducted. Gauge fixing for those theories is described by two ways.
Functional integral of superfunctions on $T_{odd}(T^{\ast}_{odd}{\cal
M}_{ext})$ is defined. Properties for generating functionals of Green's
superfunctions are studied. $\theta$-component quantization formulation,
connection with BV method and superfield quantization [3] are established.
Quantization scheme realization is demonstrated on 6 models.
