Steiner triple systems intersecting in pairwise disjoint blocks

Two Steiner triple systems (X, A) and (X, B) are said to intersect in m pairwise disjoint blocks if \A boolean AND B\ = m and all blocks in A boolean AND B are pairwise disjoint. For each v, we completely determine the possible values of m such that there exist two Steiner triple systems of order v intersecting in m pairwise disjoint blocks.