I get these large puffball type growths around my garden periodically, seemingly with no rhyme or reason. They grow to about 4inch diameter, and ultimately break (or ar broken) releasing a green-gray dust. It doesn't seem to fit exactly the typical puffball description I read about online, I live overseas in a desert climate. Any ideas greatly appreciated!
Well, I'm not from your region or climate type, so can only wildly speculate. In my region, I would be considering the possibility of a Scleroderma type of puffball, which has a thick rind, usually is aboveground or partially protruding above ground, dark mature spore mass inside. Perhaps there is something like this in your area. Also, desert regions are known for having a large variety of hypogeous fungi, also call true or false truffles. Arid areas favour fungi which have gone partially or fully underground. The only genus that comes to mind right now is Terfezia. Googling both of these genera may help, or better, speaking with mycologists in your area (University botany department or local mycological clubs) who are familiar with local fungi. Hope that is useful, frog