Integral points off hyperplanes in positive characteristic

We give a natural sufficient condition which ensures the finiteness of the number of integral points on a projective space omitting finitely many hyperplanes defined over a one-dimensional function field of positive characteristic. In this setting, when the number of hyperplanes is 2n+2, where n is the dimension of the ambient projective space, we use this natural condition to explain and sharpen an earlier result of the second named author, which provides a concrete condition on the coefficients of the linear forms producing hyperplanes such that the above finiteness property is satisfied.