My Android device may grab some 4 tasks on an odd day and while it takes more than 24 hours to complete all 4 of them running simultaneously, it was probably going to take more than 3 hours to complete their downloads this afternoon. But still they didn't download. ("The chances of anything coming from WCG / Are a million to one, but still they come!") They were stalled for some undefined time (or I wasn't aware of the correct place to look). Unfortunately, I didn't quite know how to deal with this situation; nothing that I tried had the desired effect, so I searched this forum and finally found this post by intelligently (cough, cough) applying the search term "android AND stalled".

After restarting BOINC on my phone, indeed, the tasks finally started downloading while almost 3 hours had passed since their initial aanouncement that they had been assigned to my device, waiting to be downloaded.