We investigate the electromagnetic interaction of a relativistic stellar wind with a planet or a smaller body in orbit around the star. This may be relevant to objects orbiting a pulsar, such as PSR B1257+12 and PSR B1620-26 that are expected to hold a planetary system, or to pulsars with suspected asteroids or comets. We extend the theory of Alfven wings to relativistic winds. When the wind is relativistic albeit slower than the total Alfven speed, a system of electric currents carried by a stationary Alfvenic structure is driven by the planet or by its surroundings. For an Earth-like planet around a standard one second pulsar, the associated current can reach the same magnitude as the Goldreich-Julian current that powers the pulsars magnetosphere.
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