Hi,
I am Krunoslav Vrabec from Croatia and all I can say is that VRABEC means sparrow here in Croatia too, so we come to the conclusion that Vrabec surname is from Slovak origin and spread through eastern Europe - later all over the world (but lots of them changed or modify their surnames).
All I know is that Vrabec familly's tree were basiclly peasants, farmers and hard working man.