I think with regards to Merseyrail the default to any extension will be 3rd rail. OHLE will be used if it's the line shared with mainline services. In this scenario it can be looked at as not an extension of the Merseyrail network but Merseyrail services running on the wider 'national' rail nework.
For the Northern Line, I forsee three extensions: to Skelmersdale, Burscough Bridge and to Warrington Central.
For Skelmersdale, I don't see anything but Merseyrail services using the section between Kirkby and the delta junction; calling at the new Headbolt Lane station and Rainhill on the way. The diesel service from Wigan will also be diverted to run into Skelmersdale instead of Kirkby. I'm not sure whether the line into Skelmersdale will be dual or single. I've read that the proposed services will be 2tph Merseyrail and 1tph, Northern from Wigan/Manchester with aspiration for this to increase to 2tph. A single line with such frequencies would be tricky, considering it'll be quite a good length of line. Although Merseyrail and non-Merseyrail services will share this track, I still think it'll be 3rd rail. It may be dual 3rd rail and OHLE if/when Skelmersdale-Wigan is electrified, similar to Allerton Junction-Hunts Cross. If it is dual, they may make the two tracks bidirectional, rather than just Up-Down with one being Merseyrail and other being Northern; although even then, it'll probably still be made possible for either service to use either track for the sake of flexibility.
The extension to Burscough Bridge from Ormskirk using the south curve would also only be used by Merseyrail and so would surely also be 3rd rail. This would probably be 2tph. If it couldn't justify 2tph then it probably wouldn't be worth the bother. These services might run into the Southport-bound platform and reverse, assuming it could be done without compromising the existing services on the Southport-Wigan line. Ideally, you'd have a new terminating platform. Preston trains would use the northern curve. This would terminate in the Wigan bound platform. With an hourly frequency at best and with it being a mostly self-contained line, this probably could be done without building a new terminating platform. It would also open up the possibility of Southport-Preston direct services. The connecting section between the curves that is currently in use could be mothballed, or if that's politically undesirable, maybe run one Preston train per day into Bruscough Junction (instead of Bridge) as a sort of parliamentary service. In both cases, interaction with Merseyrail is minimal. Neither Southport-Wigan nor the Preston line are electrified anyway and the latter probably will never be.
Extending to Warrington Central would probably be OHLE unless the line was given over to Merseyrail entirely. Even then, they'd probably want to keep the route as an option for diversions. I can see at least 2tph being extended from Hunts Cross, essentially replacing the Lime Street-Oxford Road services. The fact Hunts Cross has 5tph into Liverpool and Halewood only 1tph is not an accurate reflection of the difference in demand. They're very similar-sized suburbs of Liverpool and the latter has a much reduced service because of the lack of Merseyrail and the relative constraints of the CLC line with its mixed traffic; plus the flat junction at Allerton. The traffic will be slightly less mixed in the future when TPE becomes Chat Moss-only; the CLC will then be primarily a commuter and regional express line. So fewer fast trains to have to timetable the slower services around. With the stopper services going into South Parkway low level, only two trains per hour each way (EMT Liverpool-Norwich & Northern Connect Liverpool-Manchester Airport) will use Allerton Junction, so fewer conflicts with the WCML. Mossley Hill and West Allerton services could head towards Runcorn and Chester via the Halton curve, as others have mentioned.
For the Wirral Line: extension to Helsby would surely be third rail. The parliamentary service would disappear leaving only Merseyrail services (plus some freight from Shell perhaps) and Helsby has 2 platforms dedicated to this branch, allowing Merseyrail to be totally separate from the mainline. The Borderlands Line is much more complicated. It's totally self-contained so 3rd rail would work; certainly if Merseyrail only extended to Woodchurch or Helsby. If it's electrified in full, OHLE may be more beneficial considering the distance involved; although I feel it would be a poor fit for Merseyrail.
Merseyrail extensions onto the City Line are difficult to talk about for certain as we don't know exactly what they'd look like, as there are currently no official proposals. Presumably this would include connecting Liverpool Central to Edge Hill via a new tunnel and diverting some or all the Chat Moss services into it. As the underground section would be Merseyrail only, this would surely be 3rd rail. The overground section is already OHLE and so the trains would switch power at Edge Hill.
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The Abridged Version
Skelmersdale - 3rd Rail
Burscough Bridge - 3rd Rail
Warrington Central - OHLE
Helsby - 3rd Rail
Borderlands - depends
City Line - 3rd rail underground, extant OHLE overground
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AThis is borne out by data from RSSB’s safety risk model – despite the legacy DC network being only half the size of the AC network, it contributes almost eight times more (in terms of fatalities and weighted injuries per year) to overall risks on the railway. END QUOTE
I'm not convinced this tells the whole story. For a start, if we look at the AC/OHLE network as one and compare it with the 3rd rail lines then we can see they're very different in profile. OHLE is mostly used on long distance lines and relatively few commuter lines are electrified - the northern half of Thameslink perhaps being the main exception. The 3rd rail lines are mostly found in the urban South East and the Liverpool area; and so to begin with, they're within close approximation to large populations of people, increasing the chance of death by misadventure, suicides etc.
Secondly, deaths from electrocution from Merseyrail's third rail don't seem to happen very often. Whilst there may have been some recently, I'm not aware of them. The last I remember was a dog that was sited by drivers running around the underground section of the Wirral Line. Having switched off the power, they found it melted onto the power rail. The stench was unspeakable, apparently. Even that was a few years ago now. Most deaths I hear about with regards to Merseyrail involve the trains themselves; usually suicides, plus the Georgia Varley incident. Therefore, you could argue that the trains themselves are more dangerous than the power rail.
