The FOCARTA Grand Prix World Series.
complete with it's own website that I spent a lot of time on:

http://grandprixworldseries.weebly.com/
Please note the site is very much still under construction, and currently the stuff on there is pretty much everything you need to know, and nothing more.
And so, what is the Grand Prix World Series? The 26 people who enter are team principles, and each choose one of the established teams on the entrants page of the website. Many have an illustrious fictional history (this even comes with a fictional list of champions since 1950). Each team is given a budget of £50 Million to spend on two drivers, two reserve drivers, engines, and car development.
The two main drivers have to be chosen from the drivers list in the drivers market. Each have their own ratings and salary cost accordingly. Engines are also listed in the market, and each have their own cost (the price covers a full seasons' supply) and ratings. All engines and drivers are individual and different. The base cars cost £20 million, but there are also extra developments that can be made at a cost. (In the market these development costs are listed)
Reserve/test drivers can be from the drivers market (although only when the drivers market is closed) and/or drivers that you can create yourself with their own ratings, provided their mean average overall is no higher than 75. Each test/reserve driver will need to be paid a salary of £500,000.
And so how are the races run? Unlike other F1rejects series, this series doesn't use a game, but rather microsoft excel to randomly generate results, based upon the ratings of everything above. In essence, the best team will be the one with the optimal combination of drivers, car and engines. It isn't all about speed though; car reliability, driver sensibility (ie how often they do something stupid and crash into someone) etc will all play a part in the results. The type of track and the suitability of car to the track will also be a factor in results.
Obviously this is a team management game and hopefully should be quite fun. So if you want to join, take a look at the rules and info on the website, as well as picking yourself a team, your two drivers, engine supplier and any extra car developments you may want to add before season start. Prize money will be awarded for results through the season, meaning extra money for car developments if you want to further improve your car. Then just list all of your choices below, but remember drivers are on a first come, first serve basis. Engine suppliers will not supply more than 2 different teams as well. Also note that the 4 manufacturer teams each already use their own engines, and the budget is adjusted for these teams accordingly. You'll also need to give your team principle alter-ego a name.
Also take a look at the race weekend format; It's quite different to what you'd be used to. (2 qualifying races, further consolation race, the the grand prix itself for the 32 qualifiers from 52 entrants)
Or, if you can't be bothered with all that but quite like the idea of the series, put your name down anyway and I'll pick for you (Though only after everyone else has had their picks, and I will give priority of entry to those willing to choose everything straight away).
Deadline for entry and closure of drivers market for the 2012 season: 11th April 23:59
First Race weekend: 12th-15th April 2012