One MP Cost is a recurring ability in the series. Though not named until Final Fantasy X, it has been around since Final Fantasy VI. The ability enables the user to use techniques and spells at the mere cost of 1 MP, and is usually obtained late in the game due to its potency.
The ability is never named in-game, but it is the ability of the Celestriad Relic (Economizer in the original version).
An simple way to acquire a Celestriad that requires a little patience is to bet a Murakumo at Dragon's Neck Coliseum and fight the battle with Gogo giving him three steal commands, a Safety Bit and a Brigand's Glove. Let Gogo steal from the Galypdes and there is a 1/8 chance of stealing a Celestriad. The Murakumo yields a Holy Lance that can be bet to get the Murakumo back, for repeated attempts.
Celestriad can also be acquired from the Dinosaur Forest by stealing from the Brachiosaur. Easiest way is to have both Locke and Relm in the party with Locke wearing Thief's Bracer, and Relm the Fake Mustache and the Hypno Crown. Once Relm has controlled a Brachiosaur, Locke can steal his heart away. As long as no damage is dealt to the Brachiosaur, Locke can get in as many attempts as needed for a steal.
One MP Cost is an ability that can be found very rarely on dropped weapons, and can also be customized by using 20 Three Stars. It will also appear on Yuna's and Lulu's fully powered up Celestial Weapons.
One MP Cost is only available on the Font of Power Garment Grid after going through all the gates.