The choice of skill is not perfectly random whenever target foe has any non-spell skills equipped. In that case, Arcane Thievery selects a random non-empty skill slot. If this slot is a spell, it steals the spell. If not, it steals the spell on target foe's bar with the next higher skill ID. If there is no spell with a higher ID, it steals the spell with the lowest ID. If target foe has only a two spells, there can be a chance of 87.5% for one spell and only 12.5% for the other. Note that skill IDs might be different in PvE and PvP. In PvP, PvE spells affect the chances and can be stolen, but you cannot use them, except for Frustration (PvE) on the bar of HA illusion henchman Syn Spellstrike.
It is possible to steal the same spell, effectively having a multiple copy of that spell on your skillbar.
The stolen spell is linked to your attribute and not the opponent's.
The disabling effect of Auspicious Incantation does not affect Arcane Larceny. So if you use Arcane Larceny with it you can use the copied spell right away.
If you steal a maintainable enchantment, its effects will still work until you remove it, even when Arcane Larceny changes back into itself.
If you steal a copy spell and successfully copy a skill with it, it will always last the copy spell's full copy time and then revert back to Arcane Thievery, no matter how much time of Arcane Thievery is left.
During battle, if the stolen spell is from a campaign which you do not own, it will remain locked/unusable.