  Funnelling effect, in the context of searching on networks, precisely
indicates that the search takes place through a few specific nodes. We define
the funnelling capacity $f$ of a node as the fraction of successful dynamic
paths through it with a fixed target. We claim that there is a funnelling
effect if the distribution $D(f)$ of the fraction of nodes with funnelling
capacity $f$ shows a power law behaviour. We find that a transition from a
search with funnelling effect to that without any such effect can exist and is
driven by the parameters defining the network.
