I'm not sure if the Maiar were 'assigned' to the Valar or if they simply chose which Vala they wished to learn from. If the latter were true, the Balrogs would have either been orginally students of other Valar, or originally followers of Melkor, who chose his evilness to follow. He could have helped them enhance their control of fire, turning them into the balrogs we know in the silmarillion.
Its measureless plains he surveyed with the swift sight of the Valar, lying windless under the eye of Anar, or glittering under the horned Moon, or lifted in hills of wrath that broke upon the Shadowy Isles, until remote upon the edge of sight, and beyond the count of leagues, he glimpsed a mountain, rising beyond his mind's reach into a shining cloud, and at its feet a long surf glimmering.
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