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We discuss graded D-brane systems of the topological A model on a Calabi-Yauthreefold, by means of their string field theory. We give a detailed analysisof the extended string field action, showing that it satisfies the classicalmaster equation, and construct the associated BV system. The analysis isentirely general and it applies to any collection of D-branes (of distinctgrades) wrapping the same special Lagrangian cycle, being valid in arbitrarytopology. Our discussion employs a $\Z$-graded version of the covariant BVformalism, whose formulation involves the concept of {\em gradedsupermanifolds}. We discuss this formalism in detail and explain why$\Z$-graded supermanifolds are necessary for a correct geometric understandingof BV systems. For the particular case of graded D-brane pairs, we also give adirect construction of the master action, finding complete agreement with theabstract formalism. We analyze formation of acyclic composites and show that,under certain topological assumptions,all states resulting from thecondensation process of a pair of branes with grades differing by one unit areBRST trivial and thus the composite can be viewed as a closed string vacuum. Weprove that there are {\em six} types of pairs which must be viewed as generallyinequivalent. This contradicts the assumption that `brane-antibrane' systemsexhaust the nontrivial dynamics of topological A-branes with the same geometricsupport.Comment: 74 pages, 2 figure

Graded Chern-Simons field theory and graded topological D-branes