PCB via stitching for current management
The current capacity of a via is complex. The first factor is the amount of copper in the via which is determined by the plating thickness and via hole diameter. The typical plating thickness is 1 mil which equates to 0.7 oz copper. If we assume a via diameter of 10 mils, then the circumference of the via is 31.4 mils. Using a PCB trace temperature rise calculator this via could carry 1.6A with a temperature rise of 10 degrees C. However if the vias are connected to copper planes, there will be significant heat sinking and the vias could carry more current than you would expect. To make matters worse, components on the board that dissipate power will contribute to the temperature rise of the board. The most accurate way to estimate the temperature rise would be a finite element thermal analysis. I have not seen any published papers on this but I am sure it can be done but takes a lot of effort and expensive software. Another method would be to build a board and use a thermal imaging camera to measure the temperatures.