We confirm and discuss recently discovered cold HI clouds with column densities among the lowest ever detected. The column densities of Cold Neutral Medium (CNM) towards 3C286 and 3C287 are ~10^18 cm^-2, below an observational lower limit, and also below tiny-scale-atomic clouds detected by VLBI and time-variable profiles against pulsars. These column densities are close to the minimum imposed by thermal evaporation. The fractions of the CNM to total HI towards 3C286 and 3C287 are ~4% and <2%, respectively. We discuss the CNM fraction and the CNM clouds in relation to several theoretical models.
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