We discuss aspects of the possible transitionbetween small black holes and highly excited fundamental strings. We focus onthe connection between black holes and the self gravitating string solution ofHorowitz and Polchinski. This solution is interesting because it has non-zeroentropy at the classical level and it is natural to suspect that it might becontinuously connected to the black hole. Surprisingly, we find a differentbehavior for heterotic and type II cases. For the type II case we find anobstruction to the idea that the two are connected as classical solutions ofstring theory, while no such obstruction exists for the heterotic case. Wefurther provide a linear sigma model analysis that suggests a continuousconnection for the heterotic case. We also describe a solution generatingtransformation that produces a charged version of the self gravitating string.This provides a fuzzball-like construction of near extremal configurationscarrying fundamental string momentum and winding charges. We provide formulaswhich are exact in α′ relating the thermodynamic properties of thecharged and the uncharged solutions.