Which preposition to use with adjudicates

in Occurrences 11%

We have seen that minor differences may be adjudicated in each town, village and city, by justices of the peace and municipal courts; and that courts having jurisdiction unlimited as to the amount at controversy are held in every county.

on Occurrences 11%

I entered this building, where I found a bench of magistrates, the mayor of the city being amongst them, adjudicating on the cases brought before them.

as Occurrences 1%

In the first we helped Prussia to escape like a young brigand; in the second we helped the brigand to adjudicate as a respectable magistrate.

at Occurrences 1%

Sir FREDERICK COWEN, in reply to the circular, states that the closest call he ever had was when adjudicating at a Welsh Eisteddfod.

between Occurrences 1%

I heard the law, through its jury, adjudicate between a white man and a black, and sentence the latter to be flogged when the former was guiltyand they who were honest among the jurymen in vain opposed the verdict.

Which preposition to use with  adjudicates