  The configuration of typical highly excited (M >> M_s ~ (alpha')^{-1/2})
string states is considered as the string coupling g is adiabatically
increased. The size distribution of very massive single string states is
studied and the mass shift, due to long-range gravitational, dilatonic and
axionic attraction, is estimated. By combining the two effects, in any number
of spatial dimensions d, the most probable size of a string state becomes of
order l_s = sqrt{2 alpha'} when g^2 M / M_s ~ 1. Depending on the dimension d,
the transition between a random-walk-size string state (for low g) and a
compact (~ l_s) string state (when g^2 M / M_s ~ 1) can be very gradual (d=3),
fast but continuous (d=4), or discontinuous (d > 4). Those compact string
states look like nuggets of an ultradense state of string matter, with energy
density rho ~ g^{-2} M_s^{d+1}. Our results extend and clarify previous work by
Susskind, and by Horowitz and Polchinski, on the correspondence between
self-gravitating string states and black holes.
