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the highest attainable ability power by a playable champion is 1874, on Mordekaiser. To reach this amount, he must:
~have a fully stacked Mejai's Soulstealer and five Rabadon's Deathcaps.
~have a full page of Force runes.
~ have the Summoner's Wrath mastery and maximum ranks in the Blast, Mental Force, and Archmage masteries.
~possess the Exalted with Baron Nashor buff.
~have consumed an Elixir of Brilliance.
~have Ignite on cooldown.
~be affected by a Will of the Ancients aura.
~be affected by the auras of nearby Taric's Radiance and Sona's Hymn of Valor abilities, and under the effects of Lulu's Whimsy.
~have killed an enemy Karma with the same setup with Children of the Grave
This combination will result in Mordekaiser having 1874 AP. The ghost spawned will have 3448 AP, though she is not a playable character. http://leagueoflegends.wikia.com/wiki/Ability_power
This actually isn't fully accurate, as replacing 1 of the deathcaps on karma with seraphs embrace would give her an extra 9.6 ap, thus the actual total ap on mordekaiser would be 1875.76 (rounded to 1876).
Also, wouldn't a mordekaiser on karmas team who ults the mordekaiser who ulted karma have even more ap?