  We discuss graded D-brane systems of the topological A model on a Calabi-Yau
threefold, by means of their string field theory. We give a detailed analysis
of the extended string field action, showing that it satisfies the classical
master equation, and construct the associated BV system. The analysis is
entirely general and it applies to any collection of D-branes (of distinct
grades) wrapping the same special Lagrangian cycle, being valid in arbitrary
topology. Our discussion employs a $\Z$-graded version of the covariant BV
formalism, whose formulation involves the concept of {\em graded
supermanifolds}. We discuss this formalism in detail and explain why
$\Z$-graded supermanifolds are necessary for a correct geometric understanding
of BV systems. For the particular case of graded D-brane pairs, we also give a
direct construction of the master action, finding complete agreement with the
abstract formalism. We analyze formation of acyclic composites and show that,
under certain topological assumptions,all states resulting from the
condensation process of a pair of branes with grades differing by one unit are
BRST trivial and thus the composite can be viewed as a closed string vacuum. We
prove that there are {\em six} types of pairs which must be viewed as generally
inequivalent. This contradicts the assumption that `brane-antibrane' systems
exhaust the nontrivial dynamics of topological A-branes with the same geometric
support.
