The louvered metal grille that directs conditioned air from a duct into the room is called a register, and mold around an air conditioning register can have several causes:
1) If the cold air coming out of the register is too cold compared to the room air, condensate will form on the surface of the register and migrate over to the surrounding drywall. Wet drywall will begin to grow mold within a few days.
The difference between the room air and cold air coming out of the register is called the “temperature differential” or “split,” and more than about a 22º F split will cause condensate to form.
2) Duct air leakage above the register or at the connection of the duct to the register can also cause condensate to form, even if the temperature split is not excessive, because the air in the unconditioned attic or wall cavity may be significantly warmer. If squirrels or rodents get into the attic, they may shred openings in ducts for material to make their nests. Workmen in the attic also occasionally cause duct damage that leads to leakage.
3) Closing the louvers of the register completely—to shut off air conditioning to a room—can also lead to mold growth.
Mold around an air conditioning register is a good reason to call a licensed air conditioning contractor for evaluation and repair before the problem causes damage that requires more expensive mitigation.