adventitious (adj.)

Adventitious offsets are ones that occur in unexpected areas or ways.
There are apparently several ways they can manifest themselves. Tillandsia schusteri sends out a bunch of stoloniferous offsets in a way that is unusual for tillandsias. Tillandsia grandis is a terrestrial. This picture is of a very juvenile plant (prob. about six inches across) but it already has a flock of offsets.