What is the relationship between black hole mass and circumference?
Specifically, at what mass/circumference is the "surface gravity" (ie,
acceleration)immediately beyond the event horizon 1 g?

Good afternoon pericles-ga,

Taking your questions one at a time, the primary issue becomes the
definition of circumference.  As hfshaw-ga mentioned, a
commonly-accepted definition of the size of a black hole is the size
of its event horizon (the boundary at which the escape velocity is the
speed of light).  Naturally, the actual size of physical matter inside
the black hole can not be known (as no information can escape), and is
likely immaterial.  Various particles with velocities in some
distribution will exist within the black hole.  Those with greater
velocities will come closer to the event horizon (on the inside,
naturally), but there will be no solid object whose radius can be
measured.

The Schwarzschild Radius can be found by R = 2GM/c^2.  G is the
gravitational constant, M the mass of the black hole, and c the speed
of light in a vacuum.  See (
http://imagine.gsfc.nasa.gov/docs/science/know_l2/black_holes.html )
for more details.

By definition, the gravity at the event horizon cannot be 1G - it must
be sufficient that light cannot escape.  In theory at least, the
gravity may be 1G at an arbitrary distance outside the event horizon
however.  For example, a black hole exerting 1G on an object about
6.4megameters from its center would have the same mass as the earth. 
Google reports ( ://www.google.com/search?hl=en&ie=UTF-8&oe=UTF-8&q=2+*+G+*+mass+of+earth+%2F+c%5E2&btnG=Google+Search
) that the Schwarzchild radius of an earth-mass object is just under
9mm, but we know that at the surface of the earth (about 6.4megameters
from center of mass), the gravity we experience is what we call 1G.

-Haversian

Search terms:
Black hole radius
Schwarzchild radius

Black holes have the same gravitational effect as any other massive
object.  If the Earth turned into a black hole, the gravitational
force would be unchanged.  An "earth black hole" would have a
gravitational acceleration of 1g at one Earth radius from the center. 
If you were in your house, and your house somehow stayed in place
while the Earth turned into a black hole, you would feel exactly the
same force of gravity as before.

The "radius" of a black hole is usually taken as the Schwarzschild
Radius, R_s, which is equal to:

 R_s = 2*M*G/c^2

where M is the mass of the object, c is the speed of light in a
vacuum, and G is the universal gravitational constant.

The Schwarzschild Radius marks the boundary of the sphere from which
nothing can escape, i.e., the sphere with radius = R_s defines the
"event horizon").
Any object, no matter what its mass would become a black hole if it
were compressed down to a sphere with a radius less than the
Schwarzschild Radius.

As to the second part of your question, if you are asking what
mass/size black hole would have a gravitational acceleration equal to
1g at its event horizon, then there is no such combination.  Almost by
definition, the acceleration at the event horizon is infinite.  Note
that you cannot simply use the Newton's law of gravitation
(acceleration = G*M/R^2) to calculate the acceleration in this case;
one must use a general relativistic formulation (acceleration =
G*M/R^2*[1-sqrt(1-2*G*M/R*c^2)]).