Electromagnets can be created by electric current flowing through the magnetic wire wound around a metallic cylinder. The direction of the current determines the polarity of the magnets. So the direction of the movement of the charge is crucial to the determination of the polar properties of the magnetic force.
On the other hand, in the gravito magnet case, the direction of the rotation is not a factor in determining the polarity of the poles. So the similarity stops here quickly.
The following statement provides us with the current insight into the gravitomagnetism. "Gravitomagnetism is produced by stars and planets when they spin. "It's similar in form to the magnetic field produced by a spinning ball of charge," explains physicist Clifford Will of Washington University (St. Louis). Replace charge with mass, and magnetism becomes gravitomagnetism" quoted from http://science.nasa.gov/headlines/y2004/19apr_gravitomagnetism.htm.
However, there is no observed gravitational phenomenon that indicates the dipole gravito magnetic effect from a rotating spherical object as a whole. Because if that is the case, we will observe the weaker gravity force in the north pole in comparison to that of the south pole or vice versa, which has never been observed. And also the jets from the black holes would have to be only from one pole not from the both poles as observed.
The asymmetricity of the object along the rotation axis determines the polarity of the gravito magnet. For example, a cone, a hemisphere, etc will produce a gravito magnet in rotation but a rotating cylinder will not. (This point has been discussed by Bass and Pirani previoulsy where they objected that Lens-Thirring force can not be the centrifugal force because a rotating cylinder also must have a non zero Lens-Thirring force, but it doesn't. However, one can always argue that the Universe is not a cylindrical shape.)
The wider area becomes the attractive pole and the sharp and narrower area determines the repulsive pole regardless of the direction of the rotation around its symmetry axis.
The reason a spherical rotor can create a quadrupole gravito magnet is because the asymmetricity of it changes at the equatorial plane ie the radius in relative to the rotation axis increases along the Z axis and then at the equatorial plane it starts to decrease, which means that it is an oppositely stacked two dipole gravito magnets. Thus, a rotating spherical object becomes a quadrupole gravito magnet in which the equatorial plane becomes the region where the attractive gravito magnetic poles are faced to each other.
The gravito magnetic force lines come out of the both poles and merge into the equatorial plane and then joined together to come back into the center and then go back out of the both poles.
Probably 99 percent of the rotating stellar objects, if not all, including the black holes in the universe may be described as a quadrupole gravito magnet in addition to the typical gravitational monopole. When the monopole gravity dominates the gravitational interaction, the shape of the object will most likely tend to become spherical. However, as the rotational motion starts to kick in, the general shape of the star will be more like an oblate sphere or a superposed saucer shaped disk which will in turn accentuate the gravito magnetic effect and accelerate the process of becoming a black hole with enormous jets.