what determines bountiful, abundant, moderate etc. yields?

Is it random or is there something specific to this?

I get the feeling that as you get higher skill you're more likely to get the better yield missions. I cannot confirm that yet, but with two tiers open to me now I see a lot more high yield missions in the low tier than I used to.

OK, I thought it had something to do with companion's affection...

A companion's affection will make them perform better (or worse) for you, and their modifiers (+5 slicing, etc) will also affect their peformance on missions and when crafting. There is some randmomness to it, but I have found that a companion with more affection for my character and who also has the attirbute to be good at that mission is more likely to provide the high yield returns.

Companion affection and bonuses effect time spent on a mission, and perhaps their chances of bringing back better stuff.

The missions themselves are predetermined with Moderate, Abundant, Bountiful, etc. Missions come up at random.

In other words, if you do the mission "Mission of Missions to End All Missions" and it says it has a "Make It Rain! Yield" (There is no such mission or yield, it's just an example, in case that wasn't obvious...) then that mission will always have that yield when it comes up.

Note: That doesn't mean you will always get the same amount of stuff, just that it has a better chance for more stuff.