"corría por parte"
 

In the passage below, what does "corría por parte" mean?


"Acudía todos los lunes, miércoles y viernes. Su traslado desde Santiago hasta la finca corría por parte del Gallego, que delegaba la tarea en el chofer o en Fernando Apiles. El Gallego, por su parte, acudía a La Regia casi a diario, para hablar de negocios con Federico, o a disfrutar de paseos y charlas con la familia, siempre vestido muy elegante y con historias que eran del gozo de todos."

I haven't found anything specific about the expression "correr por parte de", but based on the context I think one could translate the phrase "su traslado desde Santiago hasta la finca corría por parte del Gallego" as "his travel from Santiago to the farm was handled by (was taken care of by, was organized by, was arranged by) El Gallego".

In a similar vein, the phrase can be translated as "was responsible for" («era responsabilidad»).

I agree with Wrholt and Rusty.
"Correr por parte de" is the same as "correr por cuenta de"; the expression is used to talk about someone who covers the expenses or provides the means to do something.
El Gallego paid for the trip and provided the vehicle to go to the finca. :)