Would anyone happen to know what the various game modes in the random map section actually do? I've been trawling everywhere online to try and find a manual, but no luck.

Are you asking about at random map generation screen? Or are you asking about the victory conditions where you select the sides and set the game options?

KGB

If you mean the game type in random map generation screen, this is I've been able to figure out from generating several games with different modes:

Standard: Players are randomly placed. No special rules.

Utopia: Players are all placed on the outer parts of the map. This way everbody is further away from each other and it takes longer for war to break out.

Instant Chaos: The opposite of Utopia. Everybody starts in the middle of the map, close to each other.

Clash of the Titans: Everybody starts with a level 10 hero.

Heirs to an Ancient Power: Everybody starts with a hero who has an insanely powerful artifact (like a bow that gives +5 Leadership and +8 Missiles).

North vs South: Creates two teams of 4 players. They will be allied to each other and at war with the other team. One team starts in the north, the other in the south.

Two Against the World: Creates a team of 2 players vs a team of 6 players. The 2 players start in the middle of the map.

Hammer and Anvil: Again creates a team of 2 players vs a team of 6 players. But this time the two player start on opposite sides of the map.

Against the Horde: One player is "the horde" and has a lot of cities on one side of the map and is at war with everybody else. Everybody else is allied with eachother.

Crusaders: I'm a little uncertain, but this seems to be similair to Against the Horde, except that players seem to start in random positions instead of having a team on each side of the map.

Utopia: Utopia actually puts a special city in the middle called Utopia (it has a white circle around it on the mini-map). It comes with something like +10 mana. If you capture that city and hold it for 10 turns you win the game.

Heirs to an Ancient Power is just Capture the Flag mode but you don't win by owning all the flags.

Miscellaneous:
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Utopia is broken in Email mode.

Battle of the Titans (not Clash, you are thinking of the movie is flawed in that the L10 hero comes with skills from the default sets and not from any custom army set you might create. This can lead to strange things where heroes gets skills they otherwise should not have.

KGB

Thank you so much, both of you. That was precisely what I needed to know.