  We have investigated the zero-field critical supercurrent of
YBa$_2$Cu$_3$O$_{7-\delta}$ bridges patterned from 50 nm thick films as a
function of bridge width, ranging from 2 $\mu$m to 50 nm. The critical current
density monotonically increases for decreasing bridge width even for widths
smaller than the Pearl length. This behavior is accounted for by considering
current crowding effects at the junction between the bridge and the wider
electrodes. Comparison to numerical calculations of the current distributions
in our bridge geometries of various widths yields a (local) critical current
density at 4.2 K of $1.3\times 10^8$ A/cm$^2$, the Ginzburg Landau depairing
current density. The observation of up to 160 Shapiro-like steps in the current
voltage characteristics under microwave irradiation substantiates the pristine
character of our nano bridges with cross sections as small as $50\times 50$
nm$^2$.
