  Some easily verifiable sufficient conditions for the nonexistence of
iterative roots for multifunctions on arbitrary nonempty sets are presented.
Typically if the graph of the multifunction has a distinguished point with a
relatively large number of paths leading to it then such a multifunction does
not admit any iterative root. These results can be applied to single-valued
maps by considering their pullbacks as multifunctions. This has been
illustrated by showing the nonexistence of iterative roots of some specified
orders for certain complex polynomials.
