Here's my take on it all. It'll never happen, but as has been said, it's fun to speculate:
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Emirates Brawn-Mercedes Grand Prix
1 - Jenson Button
2 - Nico Rosberg
After securing the 2009 World Drivers' Championship, Jenson Button stays on at Brawn. He is joined by Nico Rosberg after Mercedes end their relationship with McLaren, unimpressed with the way their name has been sullied by the Stepney Affair and the Australian Incident. Brawn signs Dubai airliner Emirates as title sponsor, with internet giant Google also taking pride of place alongside them.
Livery: Mercedes silver, with Brawn yellow and black breaking it up. Emirates on the sidepods, Google on the nose and rear wing.
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Red Bull Racing-Renault
3 - Sebastian Vettel
4 - Mark Webber
The Austrian energy drink consortium keeps their driver lineup from 2009, but decide to stick with Renault engines following Mercedes' decision to make Brawn their works team. Their success in stealing away the World Constructors' Championship in Abu Dhabi has drawn a number of secondary sponsors new for 2010.
Livery: The traditional Red Bull mauve and silver stays in place. Red Bull somehow convince their new sponsors to keep their logos in Red Bull colours.
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Scuderia Ferrari Santander
5 - Kimi Raikkonen
6 - Felipe Massa
It was widely exected that Ferrari would announce Fernando Alonso as one of their drivers for 2010, but everything came to naught after Alonso was implicated in the allegations of cheating levelled at Renault late in 2009. Santander are disappointed not to work with Alonso, but use Massa as a vehicle for expanding into the lucrative South American market, much as they did with Lewis Hamilton and Great Britain
Livery: Italian racing red with large Santander logos in a rather unique 'cut-off' fashion (logos intentionally larger than bodywork) that takes fans a while to get used to.
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Vodafone McLaren-Renault
7 - Lewis Hamilton
8 - Heikki Kovalainen
After a series of engine failures for Hamilton, McLaren's championship position comes under threat from Williams and Toyota. But Kovalainen rises to the occasion and secures his seat with podiums in Singapore and Brazil and a win in Japan. After Mercedes move to Brawn, McLaren turn their back on their previous partners and nominate to use the Renault engine after a gleeful Ferrari offer theirs at 'no cost'. McLaren take their Ethiad sponsorship instead, looking to start a rivalry with Emirates-backed Brawn.
Livery: Bruce McLaren's original bright orange, frequently used in testing new cars that segues smoothly into red Vodafone branding on the sidepods.
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Williams-Mercedes
9 - Rubens Barrichello
10 - Nico Hulkenberg
Williams do a do-se-do, trading Nico Rosberg for Rubens Barrichello and getting Mercedes engines in the deal. Barrichello is happy to swap as he becomes Sir Frank's lead driver, showing Nico Hulkenberg the ropes. Williams himself decides that the team's image has become too corporate and decides not to find a title sponsor to replace RBS (although the car still has sponsor branding). The emphasis on racing rather than finding a sponsor seems to rejuvenate the team, and Sir Frank is as bullish as ever.
Livery: The solid dark blue bordering on grey. Williams pick up Petronas as a sponsor after BMW's withdrawal.
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Panasonic Toyota
11 - Timo Glock
12 - Kamui Kobayashi
After trying and failing to snare Fernando Alonso after the Ferrari deal never came about, Toyota hastily sign Kamui Kobayashi for their second seat, atracting renewed interest from Japan and an influx of sponsor dollars. Glock comments that he has no idea what he is endorsing as it is all in Japanese, while pundits keep a close eye on Kobayashi; it quickly becomes known that he is operating on a race-by-race contract with Takuma Sato waiting to step up to the plate.
Livery: Toyota continue their red and white, but decide to inject a little blue into the mix. The end result is a few too many primary colours, but it is not a deviation from their standard.
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Force India-Toyota
14 - Adrian Sutil
15 - Vitantonio Liuzzi
Force India move onto their third engine supplier in as many years, following confirmation that Vijay Mallya is greatly in debt to both Mercedes and Ferrari. Toyota reluctantly take them up after Mallya manages to find a new financier. Who they are and where the money is coming from remain unknown as no new logos have appeared on the car, but speculation remains that it is a consortium led by the Indian government who have issued him an ultimatum: prove Formula One is good for India by winning a race, or else the Indian Grand Prix is shelved.
Livery: More of the same, though the white, green and orange are in equal parts.
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Scuderia Toro Rosso-Ferrari
16 - Sebastien Buemi
17 - Jaime Alguersuari
With Red Bull boss Dietrich Mateschitz going frustrated with Toro Rosso and thorwing less and less money at them, Toro Rosso slides down to the tail end of the grid. Buemi and Alguersuari are frequently seen talking with other teams, but nothing eventuates and they are condemned to circling at the back, a clear second and a half off the pace. Eddie Jordan, Aguri Suzuki and Paul Stoddart all express interest in buying the team by the third round, and negotiations continue.
Livery: The scarlet charging bull takes pride of place once more. To help distinguish the cars from the Red Bulls, black replaces the mauve and more gold appears on the wings. The car switches from Red Bull to Red Bull Cola as title sponsor.
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Telefonicia Campos-Cosworth
18 - Fernando Alonso
19 - Vitaly Petrov
Following Alonso's implication in the Singapore Incident, he struggles to find a race seat for 2010. Ultiamtely, he settles on Adrian Campos, the man who gave him his start in the World Series by Renault. Alonso later remarks that it is the best decision he has ever made, and announces a multi-year contract with a view to taking Campos to the top. With him is the other Campos collaborator, Vitaly Petrov, who brings with him an endless backing from Russian companies MegaFon and Lukoil.
Livery: Dark blue, in keeping with Telefonicia's image. MegaFon adorns one side of the car, while Lukoil graces the other. A lion and a double-headed eagle - representing the coat of arms of Spain and Russia respectively - appear as an informal team insignia between the front wheels and the sidepods.
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United States Formula One-Cosworth
20 - Pedro de la Rosa
21 - Jonathan Summerton
When Alonso joins Campos, Pedro de la Rosa is left out in the cold, but quickly snapped up by Ken Anderson and Peter Windsor. He is partnered with twenty-one year old superstar Summerton, who won his seat after a long winter testing session with Forula Two's Robert Wickens. Wickens is kept on as test driver to replace de la Rosa, who has announced he will only be racing for one year to help USF1 find their feet.
Livery: Red, white and blue, of course. The right sidepod is red, the left is blue and the monocoque is white, terminating in an arrowhead on the front wing (like one of the Le Mans cars this year).
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Virgin Manor-Cosworth
22 - Pastor Maldonado
23 - Adam Carroll
Virgin Manor becomes unoffically known as the Playboy Mansion, prompting Hugh Hefner to lend his magazine's name as a secondary sponsor. John Booth surprises all by signing two rookies, but the presence of Virgin has forged a relationship with Brawn GP, and it is believed Maldonado and Carroll come personally recommended by Ross Brawn himself. Maldonado proves to be a superstitious type and puts faith in his racing number as the car carrying the 22 has won the championship two years running.
Livery: Jet black, done to a matte finish. Looks very stealthy. Virgin name appears on red background on sidepods. As something of a novelty, the Virgin company sponsoring Manor changes every race.
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Prodrive Sauber-Mercedes
24 - Robert Kubica
25 - Bruno Senna
Peter Sauber is saved at the last minute by Dave Richards, and the two join forces to form Prodrive Sauber Sports. Robert Kubica was on the verge of signing a Renault contract when Ricahrds convinced him to stay after Renault are found guilty of cheating at Singapore in 2008. Partnered with Bruno Senna, the team attracts a lot of attention, not least of all because of thei eye-catching livery.
Livery: Gulf. That is all.
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Epsilon-Renault
26 - Nick Heidfeld
27 - Romain Grosjan
Renault is humiliated after being found guilty of cheating in 2008; Flavio Briatore is banned for life. Stripped of their 2009 points, they have the ignomity of running the numbers 26 and 27. Renault withdraw shortly thereafter and sell the team to Epsilon Euskadi. They do maintain a presence as an engine supplier, and Epsilon becomes the unofficial Renault works team. Needing money, they sign French insurance group Matmut where they beocme known as Team Warhol after the famous painter given their abstract livery. When Robert Kubica backs out of negotiations, Epsilon take Nick Heidfeld instead.
Livery: The Matmut 'patchwork'. It becomes notorious as the latest in a string of ugly liveries for the team.
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I seem to have made a very brightly-coloured grid ...
EDIT: I cannot get an image with this and I do not speak Italian, but this is an
interview with Luca and I am told that at the end he says there will be no Alonso at Ferrari in 2010.