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The purpose of this article is twofold. The first is to find the dimension of the set of integral points off divisors in subgeneral position in a projective algebraic variety $V\subset {\mathbb{P}}_{k̅}^m$, where k is a number field. As consequences, the results of Ru-Wong (1991), Ru (1993), Noguchi-Winkelmann (2003) and Levin (2008) are recovered. The second is to show the complete hyperbolicity of the complement of divisors in subgeneral position in a projective algebraic variety $V\subset {\mathbb{P}}_{ℂ}^m.$