We provide guidelines for the design and operation of a planar digital nanodispensing system based on thermocapillary actuation. Thin metallic microheaters embedded within a chemically patterned glass substrate are electronically activated to generate and control 2D surface temperature distributions which either arrest or trigger liquid flow and droplet formation on demand. This flow control is a consequence of the variation of a liquid's surface tension with temperature, which is used to draw liquid toward cooler regions of the supporting substrate. A liquid sample consisting of several microliters is placed on a flat rectangular supply cell defined by chemical patterning. Thermocapillary switches are then activated to extract a slender fluid filament from the cell and to divide the filament into an array of droplets whose position and volume are digitally controlled. Experimental results for the power required to extract a filament and to divide it into two or more droplets as a function of geometric and operating parameters are in excellent agreement with hydrodynamic simulations. The capability to dispense ultralow volumes onto a 2D substrate extends the functionality of microfluidic devices based on thermocapillary actuation previously shown effective in routing and mixing nanoliter liquid samples on glass or silicon substrates.