CommNet is a relay and control communication system implemented first in KSP 1.2 pre-release. Probe now have limited attitude and thrust control if not link back to kerbin or a control point via a relay antenna.  Antenna 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)|
|1||5Mm (halfway to Mun)||50Mm (Minmus)||~158Mm||5Gm||~15.8Gm||~22.4Gm|
|2||~15.8Mm (Mun)||~158Mm (Deep Space)||500Mm||~15.8Gm (Duna if close)||50Gm (Duna/Dres always, Jool if close)||~70.7Gm|
|3||~22.4Mm (halfway to Minmus)||~224Mm||~707Mm||~22.4Gm (Dres if close)||~70.7Gm||100Gm (Jool always, Eeloo if close)|
Each upgrade of the tracking center improves the strength of Kerbin's terrestrial-based Deep Space Network (DSN). According to the developers, range is the square root of the product (geometric mean) of the two antennas being used. Based on the provided figures, the Level 1 tracking station has an antenna strength of 70.1k, Level 2 is 223k, and Level 3 is 318k. Even the weakest relay antenna is substantially more powerful than the fully upgraded DSN.
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.