  We would like to give an overview of results on regularity, or better to say
"irregularity", properties of densities at fixed times of super-Brownian motion
with $(1+\beta)$-stable branching for $\beta<1$. First, the following dichotomy
for the density is shown: it is continuous in the dimension $d=1$ and locally
unbounded in all higher dimensions where it exists. Then in $d=1$ we determine
pointwise and local H\"older exponents of the density, and calculate the
multifractal spectrum corresponding to pointwise H\"older exponents.
