  A new infinite-size limit of strings in RxS2 is presented. The limit is
obtained from single spike strings by letting by letting the angular velocity
parameter omega become infinite. We derive the energy-momenta relation of
omega-infinity single spikes as their linear velocity v-->1 and their angular
momentum J-->1. Generally, the v-->1, J-->1 limit of single spikes is singular
and has to be excluded from the spectrum and be studied separately. We discover
that the dispersion relation of omega-infinity single spikes contains
logarithms in the limit J-->1. This result is somewhat surprising, since the
logarithmic behavior in the string spectra is typically associated with their
motion in non-compact spaces such as AdS. Omega-infinity single spikes seem to
completely cover the surface of the 2-sphere they occupy, so that they may
essentially be viewed as some sort of "brany strings". A proof of the
sphere-filling property of omega-infinity single spikes is given in the
appendix.
