You get this, right? that light travels at a certain fixed rate so TV programs (yup, light) leaving Earth in, say, 2010 would have gotten 4 light-years away and any star 4 light-years away would just be getting the program now. I’ve understood this idea for decades and I still get confused by it.
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This may only add to your confusion of the subject but just as the light year demarcation lines in the graphic expand as they get farther from earth so do the transmissions leaving earth.
The distance varies, based on intitial transmission strength, but at a certain point each transmission becomes diffuse and basically intermingles with the background noise of the cosmos and is not heard or seen in any inteligible form.
Since the switch to digital the TV broadcast would just be a jumbled mess. Unless of course the aliens signed up for a free digital converter box and had one of their alien grandkids set it up for them.