  We study the Ricci flow on $\mathbb{R}^{n+1}$, with $n\geq 2$, starting at
some complete bounded curvature rotationally symmetric metric $g_{0}$. We first
focus on the case where $(\mathbb{R}^{n+1},g_{0})$ does not contain minimal
hyperspheres; we prove that if $g_{0}$ is asymptotic to a cylinder then the
solution develops a Type-II singularity and converges to the Bryant soliton,
while if the curvature of $g_{0}$ decays at infinity, then the solution is
immortal. As a corollary, we prove a conjecture by Chow and Tian about
Perelman's standard solutions. We then consider a class of asymptotically flat
initial data $(\mathbb{R}^{n+1},g_{0})$ containing a neck and we prove that if
the neck is sufficiently pinched, in a precise way, the Ricci flow encounters a
Type-I singularity.
