That's a useful site, greasby_lad. It does tend to confirm my thoughts about boundary changes over time. When I was young, living in Ben Nevis Rd., Tranmere Hall Estate, it was definitely in Tranmere, (or Higher Tranmere), but my mother, who had ideas above her station always claimed we lived in Prenton (posher).
Historically, the Western boundary of Tranmere was Storeton Rd. beyond which was Prenton. Another boundary was Woodchurch Rd. from the Halfway House to Bessborough Rd., beyond which was Oxton. Now, according to the boundaries map, that's all Prenton, as far as Bebington Rd./Greenway Rd.
Mother will be laughing from the grave.