Which preposition to use with directly

AFTER Occurrences 1%

THE MASTER WILL BE HOME DIRECTLY AFTER THE HORSE HE BACKED HAS COME IN LAST.

OVER Occurrences 1%

He had learned the great and all-important political truth, THAT THE MORE A PEOPLE ATTEMPT TO EXTEND THEIR POWER DIRECTLY OVER STATE AFFAIRS, THE LESS THEY, IN FACT, CONTROL THEM, AFTER HAVING ONCE PASSED THE POINT OF NAMING LAWGIVERS AS THEIR REPRESENTATIVES; MERELY BESTOWING ON A FEW ARTFUL MANAGERS THE INFLUENCE THEY VAINLY IMAGINE TO HAVE SECURED TO THEMSELVES.

Which preposition to use with  directly