Third Harmonic Generation studies for monodomain nematic solutions have recently shown that biaxial anchoring conditions can be induced on the surface of nematic liquid crystals. This biaxiality relaxes in the bulk within a distance from the surface that depends both on the material elastic constants and on the degree of induced biaxiality. We compute the biaxial persistence length and predict that, by continuously varying the biaxial anchoring condition, a first-order transition occurs in the bulk from a planar to a homeotropic distribution.