  The observed near infrared background excess over light from known galaxies
is commonly ascribed to redshifted radiation from early, very massive, PopIII
stars. We show here that this interpretation must be discarded as it largely
overpredicts the number of J-dropouts and Ly\alpha emitters in ultra deep field
searches. Independently of the detailed physics of Ly\alpha line emission,
J-dropouts limit the background excess fraction due to PopIII sources to be (at
best) < 1/24. As alternative explanations can either be rejected (e.g.
miniquasars, decaying neutrinos) or appear unlikely (zodiacal light), whereas
the reality of the excess is supported by the interpretation of the angular
fluctuations, the origin of this component remains very puzzling. We briefly
discuss possible hints to solve the problem.
