It looks to me like an amaryllis??

Thank you. I looked them up and I think you're right.
These are in perforated 5 gal. buckets and have been under a mesquite tree all winter. I gather that these should probably remain as potted plants in an area of light shade and if I wanted to transplant them to nicer pots I should probably wait now till late fall.
Anyone have any experience with these in AZ?

Planted in light shade they do very well here with lots of neglect.

I think Grant posted them on another thread, maybe his "what's blooming now" thread. They are a S. African native, so this should be a pretty good area for them.

Yup, I agree with the others, it sure looks like an "amaryllis" to me (botanically called Hippeastrum). I grow many dozens of different types here and have since 2000. They love it here as long as they get some afternoon shade in summer. Just give it water when dry, regular fertilizer spring, summer and autumn, and then cut back a bit on water in winter. An eastern exposure is best (where they get sunshine from sunrise until mid-day or so). They really do great here.

I did post a few pics in the April 2012 thread, so feel free to take a look if you're curious. Other folks also posted tons of their great garden pics too. Keep us posted on how yours does for you. Happy gardening!

Here is a link that might be useful: April 2012 plant discussion

I brought some amaryllis with me from MD via NC and they bloomed in the car on the way here in March last year, but I repotted them and just got green this year. It's good to know that I can actually plant them in the ground here!