# To which character or characters does a Kleene star apply?

If you have a Kleene star applying to a set of characters not in any closure, does it apply to that whole string, or just the one character it belongs to? Any examples I search don't specify.

For example:

(A)BB*

Does this mean 1: one A followed by zero to an infinite number of BB's, or does it mean 2: one A followed by at least one B and zero to infinite number of B's?

Conventionally, the Kleene star applies only to the character immediately before it, so $ABB^*$ is $AB$ followed by some number of $B$s. Parentheses are used to make it apply to a sequence of characters; e.g., $A(BB)^*$ is $A$ followed by some number of pairs of $B$s.