I have a simple sqlite3 table that looks like this:
Table: Part
Part SuperPart
wk0Z wk00
wk06 wk02
wk07 wk02
eZ01 eZ00
eZ02 eZ00
eZ03 eZ
If you're lucky enough to be using SQLite 3.8.3 or higher then you do have access to recursive and non-recursive CTEs using WITH:

Thanks to lunicon for letting us know about this SQLite update.
In versions prior to 3.8.3, SQLite didn't support recursive CTEs (or CTEs at all for that matter) so there was no WITH in SQLite. Since you don't know how deep it goes, you can't use the standard JOIN trick to fake the recursive CTE. You have to do it the hard way and implement the recursion in your client code: