  The scaling properties of DNA knots of different complexities were studied by
atomic force microscope. Following two different protocols DNA knots are
adsorbed onto a mica surface in regimes of (i) strong binding, that induces a
kinetic trapping of the three-dimensional (3D) configuration, and of (ii) weak
binding, that permits (partial) relaxation on the surface. In (i) the gyration
radius of the adsorbed DNA knot scales with the 3D Flory exponent $\nu\approx
0.58$ within error. In (ii), we find $\nu\approx 0.66$, a value between the 3D
and 2D ($\nu=3/4$) exponents, indicating an incomplete 2D relaxation or a
different polymer universality class. Compelling evidence is also presented for
the localization of the knot crossings in 2D.
