Which preposition to use with reestablishment

of Occurrences 19%

The public mind was occasionally distracted by the current of events at Cawnpore and Lucknow, as well as at other stations which need not be particularized; but so long as Delhi remained in the hands of the rebels the native princes were bewildered and alarmed; and its prompt recapture was deemed of vital importance to the prestige of the British Government and the reestablishment of British sovereignty in Hindustan.

throughout Occurrences 1%

He had spent it entirely in two great works, the reestablishment throughout the whole of Gaul of the Franco-Gallo-Roman empire, and the driving back from the frontiers of this empire, of the Germans in the north and the Arabs in the south.

Which preposition to use with  reestablishment