When its possible that support could be offered to 2 other faction counters  fighting each other and they are asking for your support, do you have to support one side or can you choose not to support any side?

Mordante said:

From the Rules:

During the first step of combat, both attacker and defender may plead for support from all areas adjacent to the embattled area that contain a Support Order.

A player who controls such an adjacent Support order may now grant (or refuse to grant) his supporting Combat Strength to either the attacker or the defender.

Support may be given to any adjacent combat, whether a supporting player’s own forces are in the combat, or the combat is between two other players.

If there are multiple Support Orders adjacent to the embattled area, support must be declared (or refused) in turn order.

If the attacking or defending player has friendly Support Orders in adjacent areas, he may support himself in the combat (and usually will do so).

A supporting player must contribute an area’s full supporting Combat Strength, or none at all.

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The key word in all the above is "MAY".  You do not have to provide support.  You may, if you wish.

 I guess you are not asking for the rules. Basically, its up to you. You have the option to choose, support one of them or dont support anyone.

However, if two players are duking it out and you are caught around the warzone, you should support the weaker side or the side that has a general disadvantage. Why? A few reasons.

1- You dont want the weaker of the two players out of the game. The longer weaker player stalls the others, longer time you will have to backstab him.

2- If you dont support any of them, neither will be happy (if they are both asking for your support) If neither is happy with you, when they are done with each other, it is likely that they will target you. Since you did not help them, they will see it as if you helped their enemy. Therefore making you a possible enemy :)

3- In such an instance if you dont have an alliance of the game, what I do is:

If  two houses are equal of general strenght, I try to place my support such that their battle takes as long as possible. Support one then the other :) Its mean.

If one is stronger than the other, I support the weaker house to keep balance of the game and to prevent the stronger from getting more stronger.

The first, if done correctly, may not generate as much threat as supporting anyone. The second however will cause the stronger house to see you as an enemy. Will probably lead to two teams forming, WITH YOU ON THE WEAKER SIDE! Beware.

 Another question about Support.
Can a player refuse the support that someone want to give him?

 "Attacking or defending players may refuse support"

…from the rulebook