In this paper, we study the precise asymptotics of Type-IIb solutions to Ricci flow on \(\mathbb {R}^{n+1}\) . In each dimension \(n+1\ge 3\) and for each real number \(\lambda >0\) , we construct complete rotationally symmetric solutions to Ricci flow on \(\mathbb {R}^{n+1}\) that form in infinite time Type-IIb singularities with the curvature blow-up rate \(t^{\lambda -1}\) . Near the origin, the blow-ups of such a solution converge uniformly to the Bryant soliton; near spatial infinity, the solution is asymptotically flat at a precise rate depending on \(\lambda \) .
