  In this paper we prove some uniqueness results for quadratic backward
stochastic differential equations without any convexity assumptions on the
generator. The bounded case is revisited while some new results are obtained in
the unbounded case when the terminal condition and the generator depend on the
path of a forward stochastic differential equation. Some of these results are
based on strong estimates on $Z$ that are interesting on their own and could be
applied in other situations.
