  We study the size distribution of very massive close string states and the
typical string configuration as one slowly increase the string coupling, both
in the case of zero and of non-zero Neveu-Schwarz charges. The computations are
performed rigorously in string theory, starting from quantities that are
well-defined in the theory and therefore clarify previous works on the subject
which were based on various approximation techniques.
  We find that, starting from a value of the coupling in agreement with the one
predicted by the black hole correspondence principle, the string ensemble is
dominated in any dimensions by compact states whose size is within the
correspondent black hole horizon radius, which is of the order of the string
scale at the black hole/string transition point.
