Let k be an algebraically closed field of characteristic p > 0, and let C be a non-singular projective curve over k. We prove that for any real number x >= 2, there are minimal surfaces of general type X over k such that (a) c(1)(2) (X) > 0, c(2) (X) > 0, (b) pi(et)(1)(X) similar or equal to pi(et)(1)(C), and (c) c(1)(2) (X)/c(2()X) is arbitrarily close to x. In particular, we show the density of Chern slopes in the pathological Bogomolov-Miyaoka-Yau interval (3, infinity) for any given p. Moreover, we prove that for C =P-1 there exist surfaces X as above with H-1 (X, O-X) = 0, that is, with Picard scheme equal to a reduced point. In this way, we show that even surfaces with reduced Picard scheme are densely persistent in [2, infinity) for any given p.Regular 2015FONDECYTFONDECYT