truncate until delimiter

[Vadkan Jozsef <jozsi.avadkan@gmail.com>]

e.g.:

$ ls -tr `find -type f` | grep ".txt$" | rev
txt.nimdaymphp/.
txt.ccuc/aborp/.
txt.og/.
txt.osle/.
txt.kidosam/.


I Want to truncate this output, until the first "/":

$ ls -tr `find -type f` | grep ".txt$" | rev | THE-MAGIC-COMES-HERE
.
aborp/.
.
.
.

How?

I just want to modify the names of some files, but I can't do it if they
have their full path "in their names"..

Thank you!