  Quantitative models of sunspot and starspot decay predict the timescale of
magnetic diffusion and may yield important constraints in stellar dynamo
models. Motivated by recent measurements of starspot lifetimes, we investigate
the disintegration of a magnetic flux tube by nonlinear diffusion. Previous
theoretical studies are extended by considering two physically motivated
functional forms for the nonlinear diffusion coefficient $D$: an inverse
power-law dependence $D \propto B^{-\nu}$ and a step-function dependence of $D$
on the magnetic field magnitude $B$. Analytical self-similar solutions are
presented for the power-law case, including solutions exhibiting "superfast"
diffusion. For the step-function case, the heat-balance integral method yields
approximate solutions, valid for moderately suppressed diffusion in the spot.
The accuracy of the resulting solutions is confirmed numerically, using a
method which provides an accurate description of long-time evolution by
imposing boundary conditions at infinite distance from the spot. The new models
may allow insight into differences and similarities between sunspots and
starspots.
