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For D&D 4e, auras read as such:

An aura is a continuous effect that emanates from a creature. Unless otherwise noted, an aura uses the following rules.

Fills an Area: The aura fills the creature’s space and each square that is both within a specified distance of the creature and within line of effect of it. For instance, an aura 1 affects each square adjacent to the creature. A creature is normally unaffected by its own aura.

Unaffected by the Environment: The aura is unaffected by environmental phenomena and terrain, although blocking terrain blocks an aura. For instance, an aura of fire is unaffected by an area of extreme cold.

Overlapping Auras: If auras overlap and impose penalties to the same roll or game statistic, a creature affected by the overlapping auras is subjected to the worst penalty; the penalties are not cumulative. For instance, if a creature is affected by three overlapping auras that each impose a -2 penalty to attack rolls, the creature takes a -2 penalty, not a -6 penalty.

Deactivating an Aura: A creature can take a minor action to deactivate or reactivate one of its auras. However, certain auras have set durations and cannot be reactivated after they end.

Death or Unconsciousness Ends: A creature’s auras end immediately when it falls unconscious or dies.

My question is does an aura extend vertically? I'll be playing someone who can fly/hover against a homebrew creature with an aura 20. It's a nasty thing and it will be tough to avoid, I was hoping to fly to a square adjacent to the enemy 1 off the ground and avoid said aura. But, with no clear ruling I can find I'm not sure if that will work. Any ideas?

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Yes, it does.

As well as emanations and bursts, a creature's aura extends in three dimensions for the indicated number of squares.

Remember that the space occupied by the generating creature must be taken into account (as per close bursts), and that blocking terrain stops the aura.

Example 1: A Medium creature's aura 5 is a cube 11 squares on a side. The lower half is blocked by the terrain the creature is standing on; but the upper part can affect flying creatures up to 6 squares above ground.
Example 2: A Huge creature's aura 5 is a cube 13 squares on a side (5 in one direction + 3 for its space + 5 in the other direction). If the creature is flying or is in the water, its aura extends in all six orthogonal directions.

You can also check for the Tarrasque's Earthbinding aura (a 40 squares aura that prevents creatures from flying more than 4 squares above the ground). See this ancillary question.

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Tangential comments purged. For more information on the Tarrasque's aura, please see this question: Does the Tarrasque cause flying creatures to plummet to their death?. –  AceCalhoon Jan 27 '12 at 19:14
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