The largest of the rhizomatous varieties that I grow is B. masoniana, the "Iron Cross" begonia, but I'm thinking "large" in terms of leaf size. Mine has spread to a clump about 18" in diameter over several years. I suppose all of them will spread into large clumps over time, but the largest of the begonias in terms of height, etc. would be the cane types, I would think, including the taller angel wing cultivars.

There are so many that it would be hard to name some of the major ones. B. popenoi is a very large one (one I do not have). B. nelumbiifolia (water lily begonia) can get extremely large (over 2 foot across at the Miami Fairchild Tropical Garden conservatory). I have this begonia but it might approach a foot across. I have 'Caribbean Queen' and 'Caribbean King' that get to be quite large for spread and height but the leaves may only get a foot across.

The biggest one I have is B. 'Challenger'. The biggest leaf approaches two foot across and the longest petiole is close to 2.5 foot long and the diameter is almost an inch.

A huge shrub would be 'Paul Hernandez' but since you asked about rhizomatous I will stick to that category. The largest one appears to be B. parviflora from S. America although if you search for Sao Tome begonia it may be the world's largest (but no mention of it among the societies it appears).

World's largest begonia?

B. nelumbiifolia at Fairchild Tropical Gardens
{{gwi:431836}}

C. King at Fairchild
{{gwi:431837}}

No ID on this one at Fairchild
{{gwi:431838}}

Another unknown at Fairchild
{{gwi:431839}}

My C. King in 18" pot
{{gwi:431840}}

My C. Queen in 18" pot
{{gwi:431841}}

The rest are Challenger in a 15 inch pot and looks like it needs to be potted up. There are two other begonias in the same pot and the leaf size on these two are around 6 inches.

{{gwi:431842}}

{{gwi:431844}}

{{gwi:431845}}

The lens cap is 67mm (around 2.6 inches)
{{gwi:431847}}

If you are talking about bloom size, the ruffled Amerihybrids are the largest I have seen.