Unfortunately I'm not familiar with Bromeliads, so I couldn't say which one your big one is, but the small ones you picked up (love those too) are Cryptanthus, also known as 'Earth Star.' They are related to Bromeliads (I believe they are in the same family). As with Bromeliads, they bloom and die, but not before producing new "pups" to replace "Mama." I think instead of forming at the base like Bromeliads, Cryptanthus babies grow from the top of the plantand once large enough (at least 1/3 the size of "Mama"), you can remove them and root them.
Now, how to go about rooting them, I don't know.
Cryptanthus are super easy, don't water the tops like you would a Bromeliad, but the potting mix. There really isn't a cup to hold water on those anyway.
Sorry, I may be preaching to the choir, you may already know this!
Planto
