It's all about train stations this week, with the Tube bringing beauty to Battersea and Canada Water unveiling its flashy new library. Meanwhile, LA's Union Station is ripe for a revamp

Last year the mayor of London, Boris Johnson, approved the idea of building two new Tube stations on London Underground's Northern line, at Vauxhall and Nine Elms, as part of the long-awaited £5.5bn redevelopment of Battersea Power Station and the surrounding area. This is one of central London's last great wastelands. Long ripe for regeneration, developers have been wary of making a move in this surprisingly cut-off quarter of the capital despite the opportunity to build shops, offices, hotels, places of entertainment and up to 16,000 homes here – until the arrival, or solid promise, of a Tube line.

In his Autumn statement this week, Chancellor George Osborne said the government would support the scheme. Suddenly, it was easy to imagine two handsome new Underground stations, such as Arnos Grove and Southgate by Charles Holden from the 1930s, or the pick of the fine stations along the Jubilee line extension from Westminster to Stratford.

This week, however, the curiously named Battersea Power Station Shareholder Vehicle, the holding company for the forlorn former temple of power designed by Giles Gilbert Scott, was told that its lenders intend to take the 15-hectare (38 acres) site into receivership, as no progress has been made on development. This will scupper the ambitious scheme by Rafael Viñoly to revamp the listed building. Will the chancellor and mayor remain keen on building a costly Tube line to Battersea Wasteland?

In Los Angeles, the site up for redevelopment around Union Station, an exquisite late-30s design by, among others, John Parkinson and Donald B Parkinson that oozes Hollywood (the waiting area was used as a police department in Ridley Scott's Blade Runner), is even bigger than Battersea. This week, the LA Transportation Authority revealed a shortlist of architects, one of whom will masterplan the redevelopment of 17 hectares (42 acres) of downtown railway land. The shortlist includes Britain's Foster and Partners teamed with the IBI Group, and Grimshaw Architects with Gruen Associates, as well as Renzo Piano Building Workshop with Parsons Transportation Group. Architects who failed to make the list include Rem Koolhaas, Morphosis and Zaha Hadid. The plan is for mixed-use development. Will it happen? Maybe not in the current economic climate, but it would be sad if the scheme were rushed. Union Station might seem remote, even from downtown LA, but its warm, welcoming and beautifully crafted architecture could yet set a tone for LA's equivalent of Battersea.

A more modest development at a railway station opened this week in London's Docklands. This is Southwark Council's £14m Canada Water Library. Designed by Piers Gough of CZWG in the guise of a half-buried upside-down pyramid clad in a gold anodised aluminium mesh, the library is connected directly to Canada Water station on London's Jubilee line.

The shape of the building is not wilful; the plot of land – part of a new public square – was small, so Gough came up with the idea of splaying the library upwards and outwards. Unveiling the new building, Veronica Ward (Southwark's cabinet member for culture, leisure and sport) said: "What we've managed to do is listen to people. Over 6,000 people said they would rather we did things like reduce hours or use volunteers than close libraries. That was enough people saying libraries were important."

If libraries remain essential for our mental health, Maggie's Cancer Care Centres are proving to be a godsend to those seeking inspiration, support and companionship. Following the opening of the Nottingham Maggie's Centre, designed by Piers Gough and Paul Smith, the Swansea Maggie's Centre at Singelton Hospital is now complete. Set by woods and overlooking Swansea Bay, it opens officially on 9 December 2011. Designed by the late Kisho Kurokawa, one of the founders of the Metabolist movement in Japan, the building is based on Kurokawa's concept of a "cosmic whirlpool" representing "everlasting forces swirling around a still centre".

"The new Maggie's Centre will come out of the earth and swing around with two arms like a rotating galaxy," said Kurokowa. "One side will welcome the visitor and lead to the other side, which embraces nature – the trees, rocks and water. A place set apart, as Maggie [Jencks] said of a garden. The connection to the cosmos and contacts between east and west – two motives that Maggie and I shared – are in the design. I hope she would have liked it."

Meanwhile, Quentin Blake, the children's illustrator best known for his drawings for Roald Dahl stories, won this year's Prince Philip Designers prize, the last to be judged by the Duke of Edinburgh himself. Other nominees included architects David Chipperfield, Chris Wilkinson and Jim Eyre, and the engineer Cecil Balmond, co-designer of the ArcelorMittal Orbit in the grounds of the 2012 London Olympics. The structure is connected by a pedestrian bridge to Stratford station, where Jubilee line trains will take you to Canada Water, if not to Battersea.