My question isn't related to the arduino's function per se, but what I should be looking at to split the component video signals without loss of quality.
If anyone has had experience with splitting/amplifying analog video signals, could you point me in the right direction to learn more on the topic?
My limited knowledge and experience would suggest that your best bet is probably to re-purpose an existing video switcher and control it from your Arduino.
Once you get into video and audio signals doing anything "without loss of quality" isn't a straight-forward exercise. I do recollect seeing a "low tech" DIY video switcher online somewhere but it did come with warnings about noise and so forth as I recall it.
Do you have a specific reason for wanting to work at such a "low level"?
I'd be inclined to attach some optocouplers to an existing device. YMMV. 
--Phil.