| Nancy,
Different growers have different opinions as to whether to divide or not to divide. I am firmly in the "do not divide" camp (unless there is a compelling reason like the health of the plant). Cattleyatonias are fairly compact plants and clump fairly well so even when grown into good specimen size plants, they are still a managable size.
I like to leave a plant (not divide) for 2 main reasons:
1) Bigger plants seem to grow more vigorously and bloom better. Almost every cattleya alliance plant i've had, once it gets to a certain size it seems stronger and it seems to bloom bigger/better. When a plant gets to this size i say it's reached "critical mass." That's not a real term, just one i picked up at my orchid society.
2) Bigger plants make better displays. Whether you're just enjoying your plants at home or whether you're showing them, it's always nice to have lots of flowers. Bigger cattlytonias, perhaps putting out more than one new growth at a time will also put out multiple flower spikes. More growths = more flower spikes = more flowers.
Instead of dividing you could just repot your cattleytonia into a larger pot that is big enough for the whole plant to fit. Do a search on this forum and you'll find some good cattleya repotting advice.
Now I have a bit of a concern about "the dead portion in the middle." Cattleytonia growths are what we call "persistent" meaning they dont' die after they're finished. they'll stay on a plant for years. If you have clearly dead growths in the middle of your cattleytonia, there may be an underlying problem. Truly dead growths will be brown, shriveled and dry. If the plant is relatively young, sometimes the tiny growths produced when the plant was still a seedling will die off. this is normal an nothign to worry about.
There are some orchids that will die off in the middle. Cymbidiums are one of these. I think it would be unlikely to mistake a cattleytonia for a cymbidium though because they look really really different. Cymbidiums have tight round pseudobulbs and long grassy leaves.
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