a as preposition and personal a

Question

Maybe just worth pointing out that in the sentences with "a" the preposition is used in two different ways:

- as a "normal" preposition, for example, indicating motion: "El partido al que fui"

- as a "personal a", where there is a direct object (Los cantantes a los que los fans adulaban) but where "a" is needed because the object is personal.

I think that's so, isn't it?

Answer

Hola Paolo 
That is a good observation, but bear in mind those aren't the only two functions of the preposition a used with a relative pronoun. There are lots of verbs that are always used with that preposition (the same goes for "de") and their function may be different to the ones you highlight. For example with verbs like:
acostumbrarse a algo = to get used to something
referirse a algo = to refer to something
acercarse a un lugar = to approach a place/ to go by a place
So you could have sentences like:

Pedro tiene muchas malas costumbres; yo nunca me acostumbraré a la que yo considero una costumbre pasada de moda.
Pedro has lots of bad habits; I will never get used to the one I consider an old fashion custom.
 
-¿Te refieres a esa chica? 
-No, me refiero a la que me presentaste ayer.
-Are you referring to that girl?
- No, I'm referring to the one you introduced me to yesterday.
 
No vayas a esa tienda tan pequeña. Acércate a la que está en el centro, que es más grande.
Don't go to that very small shop. Go to the one in the centre, which is bigger.

I hope it helps.
Gracias y saludos
Inma