  Detecting and characterizing the anisotropy pattern of the arrival directions
of the highest energy cosmic rays are crucial steps towards the identification
of their sources. We discuss a possible distortion of the cosmic ray flux
induced by the anisotropic and inhomogeneous distribution of extragalactic
magnetic fields in cases where sources of ultrahigh energy cosmic rays are rare
transient phenomena, such as gamma-ray bursts and/or newly born magnetars. This
distortion does not involve an angular deflection but the modulation of the
flux related to the probability of seeing the source on an experiment lifetime.
To quantify this distortion, we construct sky maps of the arrival directions of
these highest energy cosmic rays for various magnetic field configurations and
appeal to statistical tests proposed in the literature. We conclude that this
distortion cannot affect present experiments but should be considered when
performing anisotropy studies with future large-scale experiments that record
as many as hundreds of events above 6x10^19 eV.
