  We extend Choptuik's scaling phenomenon found in general relativistic
critical gravitational collapse of a massless scalar field to higher
dimensions. We find that in the range 4 <= D <= 11 the behavior is
qualitatively similar to that discovered by Choptuik. In each dimension we
obtain numerically the universal numbers associated with the critical collapse:
the scaling exponent gamma and the echoing period Delta. The behavior of these
numbers with increasing dimension seems to indicate that gamma reaches a
maximum and Delta a minimum value around 11 <= D <= 13. These results and their
relation to the black hole--black string system are discussed.
