Last weekend, Transport for London (TfL) took over a new swathe of the capital's rail network, swallowing up most of the suburban lines into Liverpool Street.

It’s taken over the line to Shenfield, which will form part of Crossrail, and which for the moment it’s rebranding “TfL rail”. It’s taken over the lines to Chingford, Cheshunt and Enfield Town, all of which will become part of the London Overground. It's now going to deep clean those trains and the stations they serve, give them new branding, and ensure they're staffed at all times.

It's the same model it's followed on the earlier waves of the London Overground and it has, so far at least, been a bit of a success. Passenger surveys suggest satisfaction is high, and there's likely to be calls for TfL to take on more routes. Like this one, yesterday, from Green party London Assembly member Darren Johnson.

The obvious question, then, is – where next? Theoretically, which other routes could be added to TfL's rail portfolio?

What works

There are a number of characteristics that would make a line a good candidate for joining London's fledging S-Bahn network.

a) You want services that primarily serve suburban stations within London itself, and terminate at most a few miles outside the city limits (Transport for London can run trains to St. Albans; it shouldn’t run them in Bath).

b) You'd want them to be all-stops services, rather than the sort that speed through minor stations (a proper suburban train line shouldn't just try to get to stations where ticket prices are higher as quickly as possible).

c) And you'd want them to have their own tracks, wherever possible. This means you can muck around with timetables and so forth without having to worry too much about cocking up long-distance services. It should make it easier to separate out the suburban bit of the existing franchises from the regional bit, too.

That's a lot of variables to consider. And we're quite lazy round here.

So it's lucky, on the whole, that someone else has already done the work for us. To be specific, NERA Economic Consulting, who produced this report for TfL London Rail in 2011. (Hat tip: The very fine London Reconnections website.)

Here's what they came up with:

This map is a bit out of date – in the west, it only shows Crossrail extending as far as Maidenhead, rather than to Reading – but it gives some sense of the possible scale of TfL’s ambitions here.

What's in

Being dedicated CityMetric readers, you can no doubt identify any railway line in London, even from a map as blurry as this. But just in case you can't, here's a brief rundown of the lines shown in purple to idenfity them as potential targets, with some close ups so you can make out the labels. Starting in the north and moving clockwise, we have:

1. Thameslink's more suburban services, from Luton and (one day) Welwyn Garden City, across town to various destinations in south London, Surrey and Kent;

2. The Hertford loop line, from Stevenage into Moorgate;

3. The Lea Valley lines into Liverpool Street. Most of these came into TfL's hands over the weekend, but this map suggests the route from Stratford to Hertford, via Tottenham Hale and Cheshunt, as another possible candidate;

4. The lines currently operated by South Eastern trains, from London Bridge or Victoria out to Dartford, Sevenoaks, Orpington and Hayes;

5. The Southern routes, to Croydon, Sutton, Epsom and beyond;

6. The South West Trains suburban network from Waterloo, to the Surrey suburbs.

Which is potentially rather a lot of trains.

What's out

So what isn’t included? Mostly the lines in grey are the slightly longer distance trains, that exist primarily to serve commuter towns rather further from the city itself.

But all the lines into two entire mainline stations – Fenchurch Street and Marylebone – are also left out of the fun. At first glance, that seems a bit unfair.

Actually, though, what those two lines have in common is that their suburban services are already run by TfL – were swallowed up by the District and Metropolitan lines respectively, well over a century ago – leaving them only with longer distance trains.

That means that there are a few London stations – places like Dagenham Dock and Northolt Park – that are exceptionally unlikely to ever join the orange revolution. There are a few other stations in the outer reaches of south London – Sanderstead, Coulsdon South – that would excluded, too, purely because they’re on branches only served by longer distance trains. Which is kind of sad, but, them's the breaks.

Perhaps the oddest exclusion is the branch line from Ealing Broadway to Greenford. That's well inside the city boundary, branching off a line that's on course to become part of Crossrail – yet for reasons we can't quite fathom looks set to remain outside TfL's hands.

Were all this to go through, the result would be that every station in Greater London would be served by TfL trains, with just 13* exceptions.

This map, as noted, is four years old. It’s already out of date. A few of the lines marked as targets have now actually joined the Overground. And TfL has already tried to take over the suburban services provided by Southeastern, but was rebuffed after opposition from Kent MPs.

Nonetheless, this is a pretty good guide to what London's transport authorities could one day run, if a government was so minded. We can but dream.

*For those who are wondering: Drayton Green, Castle Bar Park, South Greenford, Wembley Stadium, Sudbury & Harrow Road, Sudbury Hill Harrow, Northolt Park, Dagenham Dock, Rainham, Sanderstead, Riddlesdown, Upper Warlingham, Coulsdon South.