ITS WAR between Iraq and Iran. Ostensibly it's over the dispositin of a contested estuary. Actually it's over who's top dog in the Persian -- to Iran, Arabian to Iraq -- Gulf. Iran, while it had the military edge in the 1970s, pressured Iraq to accept an estuary agreement that Iraq, now that it has the edge, demands to revise. Then Iran was playing an ethnic card, stirring up Iraq's Kurds, and now Iraq is playing an ethnic card, encouraging Iran's Arabs. Just who started the shoving match that escalated yesterday to "full-scale war" is anyone's guess. But Iraq, like everyone else, can see that Iran's revolution has vitiated its army and alliances. Ayatollah Khomeini, moreover, had long been preaching revolt to the Shiite half of Iraq's Moslems.

According to the conventional wisdom, the kind and quality of armed forces of the two countries and the nature of their rivalry will make for a short spasm of a war. But no prudent person should count on it. In addition to the lives at stake, there is too much crockery around available to be broken in the way of oil facilities and the quiet needed to operate them. Only a predator would want to see violence confirmed as a method of sorting out the national and ethnic rivalries of the Gulf. Iran's Shiite revolution has alarmed other Moslem states of the region, Arab and non-Arab, but they are no more pleased to see among them, Soviet-armed Iraq, rising to a position of military domination. Would-be mediators have their work cut out for them. The United Nations was the proud matchmaker of the 1975 estuary agreement. Can it patch it up?

Through the "twin pillars" of Iran and Saudi Arabia, the United States used its influence through the 1970s to keep the dust down in the Gulf region. But Iran has collapsed as a pillar and the Saudis nervously evade the role. Relations between the United States and Iraq are, in good times, cool, narrow, wary. In regard to this war, there is scarcely a conflict anywhere that Washington is in a poorer position to help ease.

The United States has argued for some time, to Iran and to itself, that the holding of the hostages was distracting the Khomeini regime from more important national cares, such as maintaining the integrity of the country. Whether Ayatollah Khomeini is coming to see it that way, or whether his taste for tension and martyrdom has merely been sharpened, is not the least important question posed by the new war.