In My Hero Academia, chapter 6:
Midoriya throws the ball, and Aizawa erases his Quirk, making him fail a first time.
During this time, he grabs the student with his scarf, while not touching it. The drawn version is ambiguous, but the anime version is clear about that statement.
How so ? His quirk is only quirk erasing, not something about gravity or scarf controlling. Is there even a valid reason about that ?
Links to evidence:
Aizawa-sensei's quirk is Erasure:
Shota's Quirk gives him the ability to nullify anyone's Quirk by looking at them.
The cloth like material is not a quirk nor is it quirk controlled. It is called the Capturing Weapon:
The Capturing Weapon is a cloth-like equipment made from carbon fibers and a special metal alloy. Shota Aizawa wears it around his neck at all times.
He is able to manipulate the weapon to ensnare his targets and immobilize them. He uses the weapon as a powerful combo with his Erasure Quirk and as a precaution for Mutant-type Quirk users who are immune to his nullification power.
