Here's the actual truth, from someone who actually did the grind to fill mats of all classes (long post - bereft all hope thee who... y'know):
Let's formalize some things first:
1. Combat Aftermath does not yield materials anymore, at max a mini-mission for some faction where you have to recover data from a derelict ship.
Ironically, if you read the game help, pharmaceutical isolators, improvised components and military supercapacitors were all found at the Combat Aftermaths in the past, so you know where the shortage come from.
2. Raw materials of all classes - easily found on worlds with Bio/Geo features (see the Sanguineous Rim method).
3. Currently I don't know and I don't think there is a sure-fire method to acquire Data materials, unless of course playing the game (what means scanning ships/high wakes, scavenging POI's or doing settlement missions) or using the materials trader, what brings us to...
4. Manufactured materials, the only ones that can't be farmed on HGE or USS are the Biotech Conductors (maybe Exquisite Focus Crystals as well I don't really know). I never saw any mission handing out military supercapacitors, honestly, but the galaxy is a big place.
5. From observation, HGE are easier to spawn on highly populated systems (> 3m for the absolute minimum, the more the better). Also it HAS TO HAVE high traffic ( ideally >150 ships), otherwise you'll have to spend much more time waiting around for HGE to spawn.
6. Also, from observation, it is easier to HGE to spawn for the controlling faction then it is for the others (from now on, always suppose the results are from observations unless stated otherwise).
7. Since materials are apparently dependent on faction affiliation first, then state of the faction, you'll want to search for these on independent systems with the majority of it consisting of independent factions as well, otherwise you will get more CD Composites and Imp Shielding than anything. On independent systems, the chance of spawning Thermic Alloys, Proto Heat Radiators etc... are higher than spawning MS's, PI's or IC's so... account for that.
8. For some reason, player interactions with the BGS generate more BOOM state systems than anything else, so you may have to take a road trip.
9. There's that trick when you find very rare materials where you Alt+F4, and, you know....
Now the catch-22:
Since there's a higher chance for HGE's to spawn for the controlling faction than the other ones, you want it ( the controlling faction) and, ideally, some other faction sharing the state of the material you're looking for.
So suppose you're looking for Pharmaceutical Isolators (PI's). You'll want ideally an independent or allied system where the controlling faction is on Outbreak, where there's more independent factions than empire or federation ones and ideally where some of those factions are also on Outbreak (you can use Inara.cz to search for that).
I am under the impression the MS's, PI's and IC's HGE last shorter than the others. They last about 15 mins when other HGE last 25-30 mins, so there's that. When you find a 15 min HGE that you didn't scan before 9 out of 10 is what you're looking for.
So, to sum up:
- High population, high traffic (>3m, >150 ships)
- Correct faction affiliation, (no feds or imperials controlling the system)
- Correct faction proportion, (more independent or allied factions than anything else)
- Correct faction state proportion. (more factions sharing the same status than anything else)
P.S.:
PI - Pharmaceutical Isolators. Found at Outbreak systems (High Grade Emissions).
MS - Military Supercapacitors. Found at War/Civil War systems (High Grade Emissions).
IC - Improvised Components. Fount at Civil Unrest systems (High Grade Emissions).
Rare materials like Heat Vanes are found at Encoded Emissions under the same conditions.
You can also get these materials by pirating haulage vessels (and destroying the ship afterwards) on Outbreak/Civil Unrest systems or actually attacking authority ships on War/Civil War systems OUTSIDE the CZ's (I did not do the latter, but pirating I did and it worked, and, presumably, by extension, destroying authority ships should also work (beware of the bounties though)).
Using the strategies above plus the Alt+F4 trick, I maxed out all components in three days. So good luck to y'all (or use the materials trader)