Fibrous rooted begonias generally describe canes and semperflorens. I think it would be better to talk about growing habits instead of root systems.

The ones that die back (go dormant) in fall are tuberous. Rexes can defoliate in fall but should not be treated as dormant like tuberous. Not all rexes drop all their leaves if they have good light. Rhizomatous and canes can drop a lot of leaves - some of it is in response to an environmental change like moving from outdoors to indoors, not enough light, or it is time to shed old leaves and put out new leaves.

Rhizomatous is a category of begonias where the stem grows along the ground (like a bearded iris - a rhizome). Marmaduke and Tiger Kitten are rhizomatous and should do well for you if you provide good conditions such as ample light and humidity.

Thanks HMC...one more question.

I ended up ordering both Marm and Tiger Kitten Begonias. They will will be potted in containers. Since their stem/root? sytems grow along the ground, should I use a wide/shallow pot or does it matter?
Do they prefer being rootbound?
Neither begonia is hardy to my zone which is 5.

Oh another question..lol..Do Rhizomatous Begonias need as much/more/less humidity than a Rex? Thanks so much, Toni

Toni,

A wide bowl (bonsai or azalea pot) would work well with rhizomatous begonias. In California I saw a Marmaduke planted in a wide coir-lined hanging basket. It filled it very nicely.

A standard pot will work as well but the rhizomes will eventually creep over the edge of the pot which makes it easy to snap off long rhizomes and start new plants.

Rootbound is okay but after a couple of years you may want to repot it. You don't want to overpot it especially in winter. A big pot in summer (if it doesn't stay wet all the time) will allow the plant to grow to a much larger size. Tiger Kitten should stay in a smaller pot until it fills it due to its smaller nature.

There are very few begonias hardy even in my zone (7) let alone 5. The option is to always keep them indoors but I prefer to move them out for summer and in for winter.

Most begonias can take "normal" house air, even rexes. There are some exotic ones that just need to go in a terrarium in my opinion. Just don't let them dry out completely and water deeply when you do. A fast draining potting mix is preferred. I've had much better luck with these watering methods than in the past (too wet or too dry).