  Two surfaces are "sticky" if breaking their mutual contact requires a finite
tensile force. At low fractal dimensions D, there is consensus stickiness does
not depend on the upper truncation frequency of roughness spectrum (or
"magnification"). As debate is still open for the case at high D, we exploit
BAM theory of Ciavarella and Persson-Tosatti theory, to derive criteria for all
fractal dimensions. For high D, we show that stickiness is more influenced by
short wavelength roughness with respect to the low D case. BAM converges at
high magnifications to a simple criterion which depends only on D, in agreement
with theories that includes Lennard-Jones traction-gap law, while
Persson-Tosatti disagrees because of its simplifying approximations.
