  We consider the hierarchic tree Random Energy Model with continuous branching
and calculate the moments of the corresponding partition function. We establish
the multifractal properties of those moments. We derive formulas for the normal
distribution of random variables, as well as for the general case. We compare
our results for the moments of partition function with corresponding results of
logarithmic 1-d REM and conjecture a specific power-law tail for the partition
function distribution in the high-temperature phase. Our results establish a
connection between reaction-diffusion equations and multi-scaling.
