I noticed today at New Malden, the 'on' logo is still on the pole outside
the station under the NR logo, and the 'on' underground style route maps are
still on the platforms. Are there many other stations showing this out of
date stuff, and are TfL likely to go round and remove it all at some stage?

Paul

No they won't.

See Wikipedia.

"According to a talk given by Innes Ferguson of TFL at the London
Transport Museum on 24 September 2007 the Overground Network scheme is
now "dead", the logo is no longer being used on Train Operating
Companies' (TOCs) publicity material nor is the network being promoted
by TFL. He added that whilst TFL funded the installation of Overground
Network "on" signage at appropriate National Rail stations, it is
being left to individial TOCs to remove these at their own expense,
hence the many that remain in situ as of October 2007."