This is a good question Maria and I have not come across fixed rules.
Here are my thoughts
When you are chatting socially if the station name is an acronym or abbreviation then with and without the article are both acceptable: ABC/the ABC e.g. I�m watching "....." on the ABC/ABC tonight.
However, as Paddy has written, an article is often used in the business sense e.g. The political debate will be aired on the ABC.
However, if the station name starts with �channel� then no article is required: Channel 10 (not the channel 10) e.g. I�m watching "....." on channel 10 tonight. The political debate will be aired on channel 10. (n.b. some will reduce this to just the number e.g. I�m watching "....." on 10 tonight. The political debate will be aired on 10.)
My favourite TV stations are ABC and channel 10
My favourite TV stations are the ABC and channel 10
If the name is a proper noun then just apply the general rules for articles (no article) e.g. I�m watching "....." on Prime tonight. The political debate will be aired on Prime.
The same applies for radio stations.
This is my understanding and I hope my thoughts are of assistance.
Thanks for the interesting links Douglas.
Cheers
Jayho