  In this paper, we study the precise asymptotics of noncompact Type-IIb
solutions to the mean curvature flow. Precisely, for each real number
$\gamma>0$, we construct mean curvature flow solutions, in the rotationally
symmetric class, with the following precise asymptotics as $t\nearrow\infty$:
(1) The highest curvature concentrates at the tip of the hypersurface (an
umbilical point) and blows up at the Type-IIb rate $(2t+1)^{(\gamma-1)/2}$. (2)
In a neighbourhood of the tip, the Type-IIb blow-up of the solution converges
to a translating soliton known as the bowl soliton. (3) Near spatial infinity,
the hypersurface has a precise growth rate depending on $\gamma$.
