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.
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