CommNet is a relay and control communication system implemented first in KSP 1.2 pre-release. Probes now have limited attitude and thrust control if they are not linked back to Kerbin or a control point via a relay antenna.  Antennae have limited range from which control and transmission of science data is possible.
|Tracking Station Level||5k (Probes / Manned)||500k (Communotron 16)||5m (HG-5 High Gain)||5b (DTS-M1 / RA-5)||50b (HG-55 / RA-50)||100b (Communotron 88-88 / RA-100)|
||5Mm (halfway to Mun)||50Mm (Minmus)||~158Mm||5Gm||~15.8Gm||~22.4Gm|
||~15.8Mm (Mun)||~158Mm (Deep Space)||500Mm||~15.8Gm (Duna if close)||50Gm (Duna/Dres always, Jool if close)||~70.7Gm|
||~22.4Mm (halfway to Minmus)||~224Mm||~707Mm||~22.4Gm (Dres if close)||~70.7Gm||100Gm (Jool always, Eeloo if close)|
Each antenna has a "strength rating" measured in meters. It ranges from 5k (5000m) for integrated default antennas available in every spacecraft, to 100G (100 billion meters) for the largest dishes. A connection can be estabilished between two stations (craft to ground, or craft to relay) when the square root of the product of the strength ratings is greater than the distance between the two objects. When a craft has multiple antennas, all the strength values are summed to obtain the craft strength rating.
An early probe with two Communotron 16 whip antennas has a rating of 1Mm (2 x 500km). The dishes of the basic tracking station have a rating of 5Gm; their product is 5x1015 m2, and the maximum range is 70.71x106 m = 70710 kilometers; enough to control a probe in Minmus orbit, but not outside the SoI of Kerbin.
Each upgrade of the tracking center improves the strength of Kerbin's terrestrial-based Deep Space Network (DSN). Based on the provided figures, the Level 1 tracking station has an antenna strength of 5G, Level 2 is 50G, and Level 3 is 100G. This is equal to the small, medium and large relay antenna ranges respectively.
The same document from the KSP developers states that science returned via a relay satellite will have a bonus applied (some fraction of the difference between the recovery and transmission science potential). The exact amount of the bonus depends upon signal strength.
These figures may change with the final release of 1.2.