How to care for Amaryllis offshoots?

[Vesper]

I bought a blooming amaryllis from walmart last year in late fall. When the flower died, I cut off the stalk, and have since been watering lightly and letting the leaves grow under fluourescent lights. About a week ago I noticed a small leaf shooting up totally apart from the main plant. Does this mean that there is a new bulb growing on the original one? And if so, should I seperate this bulb or leave it? Will the offshoot flower along with the original plant?

[bullthistle]

I would let the bulbet mature more before breaking it off from the main bulb. Like after the next bloom period or after then break it off.