In piezo inkjet printing, nozzle failures are often caused by an ink layer on the nozzle plate. It is experimentally shown that the ink layer at the nozzle is formed through streamers of ink, emanating from a central ink band on the nozzle plate. The streamers propagate over a wetting nanofilm of 13 nm thickness, directed toward the actuated nozzles. The motion of the front end of the streamers follows a power law in time with an exponent ½. The observations are consistent with a surface tension gradient driven flow. The origin of the Marangoni flow is an effective lower surfactant concentration of the ink around the nozzle.