  This article deals with the existence and the uniqueness of solutions to
quadratic and superquadratic Markovian backward stochastic differential
equations (BSDEs for short) with an unbounded terminal condition. Our results
are deeply linked with a strong a priori estimate on $Z$ that takes advantage
of the Markovian framework. This estimate allows us to prove the existence of a
viscosity solution to a semilinear parabolic partial differential equation with
nonlinearity having quadratic or superquadratic growth in the gradient of the
solution. This estimate also allows us to give explicit convergence rates for
time approximation of quadratic or superquadratic Markovian BSDEs.
