At last a unified London Connection Map

http://www.nationalrail.co.uk/passenger_services/maps/London_Rail_Tube_map.pdf

The National Rail website "London's Rail & Tube services map (which replaces the former London Connections map) shows all National Rail routes and stations within the Greater London area, together with London Underground, Docklands Light Railway and London Tramlink services and stations.
The map highlights principal interchange points and London Fares / Travelcard zones. It also shows the extent to which Oyster pay as you go is valid.
Leaflet copies of this map (with the London & South East map below on the reverse) are normally available from staffed National Rail stations in London and the South East and should now also be available from most London Underground stations."

Should say "replaces the former London Connections Maps" as for many years TfL (and its antecedents) puboished a map under this title. It was fairly recently displace by a  map showing where Oyste PAYG could be used. Nevertheless, I welcome at long last one map (not two rivl versions) showing all London's Railways, along with the zones.

"Should now be available from most London Underground stations" is rather tentative, but the old ATOC map (and antecedents) never was. Is there reluctant acceptance that public  transport is about where people want to go, and not about who runs which railway?

Oyster PAYG on National rail from 2008

http://www.tfl.gov.uk/assets/downloads/tickets/oyster-PAYG-08-01-02.pdf

The new map is here

Oyster PAYG rail network

I have coined this phrase on Wikipedia (assuming the editors don't eradicate it) for brevity, to cover the rail lines on which Oyster Pay as you go PAYG is valid, namely:

London Underground
DLR
London Overground (opens 11/11/2007)
Certain parts of certain National Rail lines, as published.

Which is all a bit of a mouthful.

[The parts of National Rail lines that accept Oyster PAYG are those that have historically accepted LU fares, because they parallel Underground routes. See http://www.tfl.gov.uk/tickets/oysteronline/5823.aspx for full details.]