  \def\R{\mathbb R}
  We give a characterization of G-regularity for super-Brownian motion and the
Brownian snake. More precisely, we define a capacity on $E=(0,\infty)\times
\R^d$, which is not invariant by translation. We then prove that the hitting
probability of a Borel set $A\subset E$ for the graph of the Brownian snake
starting at $(0,0)$ is comparable, up to multiplicative constants, to its
capacity. This implies that super-Brownian motion started at time 0 at the
Dirac mass $\delta_0$ hits immediately $A$ (that is $(0,0)$ is G-regular for
$A^c$) if and only if its capacity is infinite. As a direct consequence, if
$Q\subset E$ is a domain such that $(0,0)\in \partial Q$, we give a necessary
and sufficient condition for the existence on $Q$ of a positive solution of
$\partial_t u+{1/2}\Delta u =2u^2$ which blows up at $(0,0)$. We also give an
estimation of the hitting probabilities for the support of super-Brownian
motion at fixed time. We prove that if $d\geq 2$, the support of super-Brownian
motion is intersection-equivalent to the range of Brownian motion.
