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We study the dependence on various parameters of the exceptional set inVojta's conjecture. In particular, by making use of certain elliptic surfaces,we answer in the negative the often-raised question of whether Vojta'sconjecture holds when extended to all algebraic points (that is, if theconjecture holds without fixing a bound on the degree of the algebraic points).

The exceptional set in Vojta's conjecture for algebraic points of bounded degree