Is there a maximum size for a single snowflake?
According to Caltech physics professor Kenneth G. Libbrecht's site SnowCrystals.com


  This monster is, to my knowledge, the largest snow crystal ever photographed. It measures 10.1 mm (0.4 inches) from tip to tip (averaged over the three axes). ... Note that this is a snow crystal: a single crystal of ice ... Larger snowflakes have been reported, but those were puffballs made of huge numbers of individual snow crystals stuck together. During very calm conditions, these puffballs can grow into pancake-shaped agglomerations as large as a dinner plate 


He has a paper Physical Dynamics of Ice
Crystal Growth, but I don't see any discussion of theoretical maximum sizes of crystals or agglomerations.