And I believe I've just found my answer:
This is broadly right, wherever you found it, but there are some subtleties it misses, and a lot of pre-3.3 information which is out of date - I'll try to cover the bits it's missing.
Some information said:
A faction will attempt to expand to a new system when their influence reaches 75% in a system and they are not being blocked by a conflict state.
As of the 3.3 release, conflict states no longer block expansion. Though you will have difficulty getting to 75% influence while in a conflict state in the same system, of course, due to the influence lock ... you can start a conflict after the expansion has gone pending and it won't interfere with the expansion.
Some information said:
At the end of the expansion state the faction attempts to expand to the nearest system within 20ly fewer than 7 factions present
"within 20LY" is imprecise - the expansion range is measured on a cube with the centres of each face 20LY from its centre (i.e. a cube with sides 40LY long centred on the expansion system) which is aligned to the galaxy map grid. This means that expansions up to ~34LY are possible if the target system is in the correct direction.
Additionally, at this stage factions will try to avoid systems they have already retreated from - any previously-retreated-from system will be considered to be further away than any fresh system. How recently the retreat was, and whether the faction has retreated from it once before or ten times before, doesn't matter.
Some information said:
and if successful loses 15% of their influence in the system they expanded from.
Slightly surprisingly for information that mostly seems to be pre-3.3, this is correct and was added in 3.7 just a few months back.
Some information said:
During the expansion state, they gain bonus influence for actions in that new system.
I'm not sure what this is trying to say but it doesn't sound right.
Some information said:
If there is no valid system within 20Ly the expansion will fail and the faction will go into an investment state where actions will allow the next expansion to reach 10ly further.
Since 3.3 failing to expand no longer triggers an investment state - Investment is now caused by high levels of positive economic activity and does not affect expansions at all. The range is still extended, but this is not marked by any special states.
Some information said:
If a system is full but there is a faction with very low influence presence the expansion will work and immediately trigger an invasion war in the new system.
"very low influence presence" is true but incomplete - there are further conditions:
- the target faction must not be native to the new system
- the target faction must not already be in, pending or recovering any sort of war or election
- the target faction must have the lowest influence of all target factions allowed by the above rules in the entire expansion cube - it's not the nearest ... but equally the target influence can be very high in some cases.
Some information said:
During the expansion state, the faction will offer expansions missions and ask for exploration data to be sold at the system they are expanding from. These actions have an unquantified positive effect on the starting influence in their new system.
This may no longer be true. If it does still work, the effect is now fairly subtle.