  We study the explosion phenomenon of nonlinear continuous-state branching
processes (nonlinear CSBPs). First an explicit integral test for explosion is
designed when the rate function does not increase too fast. We then exhibit
three different regimes of explosion when the branching mechanism and the rate
function are regularly varying respectively at $0$ and $\infty$ with indices
$\alpha$ and $\beta$ such that $0\leq\alpha\leq \beta$ and $\beta>0$. If
$\alpha>0$ then the renormalisation of the process before its explosion is
linear. When moreover $\alpha\neq \beta$, the limiting distribution is that of
a ratio of two independent random variables whose laws are identified. When
$\alpha=\beta$, the limiting random variable shrinks to a constant. Last, when
$\alpha=0$, i.e. the branching mechanism is slowly varying at $0$, the process
is studied with the help of a nonlinear renormalisation. The limiting
distribution becomes the inverse uniform distribution. This complements results
known in the case of finite mean and provides new insight for the classical
explosive continuous-state branching processes (for which $\beta=1$).
