As the Yeltsin-era oligarchs have declined, the "state" oligarchs have emerged. One reason is Mr Putin's propensity for using trusted acquaintances or former KGB colleagues in every aspect of his attempt to re-establish state power. He packed the presidential administration and government with them - and increasingly in his second term has given the same people supervisory roles in state business.
The second is the still largely unacknowledged policy of using state businesses to re-establish Kremlin control of strategic assets. Sometimes, as with Rosneft's purchase of the main production arm of Yukos in 2004, or Gazprom's acquisition of Sibneft from the UK-based Roman Abramovich, this has amounted to a renationalisation of assets privatised in the loans-for-shares scheme. In other cases, state-controlled assets are being regrouped into national champions in airlines, aviation or nuclear power (see below).
Andrei Illarionov, Mr Putin's former economic adviser turned Kremlin critic, says Russia's ruling apparatus has turned into a kind of corporation. "The main incentive for a corporation member is the prospect of being placed in charge of a state-controlled company; the size of that company's financial flows is the most accurate indicator of that person's place in the corporate hierarchy," he says.
On the other hand, Mr Medvedev - a leading contender to succeed Mr Putin - tells the Financial Times: "I don't believe we're seeing any significant increase in the state's participation in business.
"True, in a number of cases, state-controlled companies increased their presence. Above all we're talking about the energy sector. But we're not talking about nationalisation but about buying appropriate assets on the market."
Dmitry Peskov, a spokesman for Mr Putin, says he "categorically does not agree" that a new oligarchy has formed in Russia - although he makes no bones about the fact that many senior officials and associates of the president hold positions in state companies. The officials, he says, rightly represent the state's interests. "These people are not businessmen; they don't have operational control of the company."
As for managers such as Gazprom's Mr Miller or Russian Railways' Mr Yakunin, he - like other senior officials - says it is not unusual in Europe or North America for big companies to be run by people who happen to know the country's leader. "Gas and railways are life-and-death industries for a country the size of Russia," says Mr Peskov. "Whether Mr Yakunin is a friend of the president is of minor importance. What is important is whether he is a good manager."
But FT research has found Russian officialdom and business to be extraordinarily intertwined. Of its presidential administration, 11 members chaired six state companies and had 12 further state directorships; 15 senior government officials held six chairmanships and 24 other board seats. In no other G8 country do ministers or senior aides to the head of state or government sit on government companies' boards.
The state has also become a big player in mergers and acquisitions. Two transactions - its move to increase its stake in Gazprom from 38 to 51 per cent and Gazprom's purchase of Sibneft - totalled $20.21bn, or half the $40.5bn value of all Russian M&A deals last year, according to KPMG. Figures from the European Bank for Reconstruction and Development show the public sector's share of the economy rose from 30 per cent to 35 per cent last year.
Just like the rise of the 1990s-era oligarchs, the increasing role of state business and its directors has important implications. It does not represent a return to Soviet-era central planning. The Kremlin has embraced the market - as demonstrated by the planned Rosneft IPO and its move to lift restrictions on foreign investors buying the 49 per cent of Gazprom shares not owned by the state. But the new model is a much more directed capitalism.
Take aviation. As Chris Weafer, chief strategist at Alfa Bank (owned by Mikhail Fridman, another 1990s oligarch), points out, in order to recreate a national carrier, Aeroflot is being reunited with several regional airlines carved out of it in the 1990s. Instead of replacing its ageing fleet with Boeings or Airbuses, it may buy aircraft from United Aircraft Corporation, the national aviation giant now being formed. UAC may, in turn, buy parts from VSMPO-Avisma, a privately owned world leader in titanium that also seems set to fall under state control. Throw in the possibility that windfall oil revenues sitting in Russia's $60bn "stabilisation fund" could rebuild crumbling airports and the vision of state capitalism takes shape.
There are risks in such an approach. Around the world, public ownership has generally been less effective than private. Instead of focusing on areas where Russia has real global advantages, the state might focus on propping up ailing dinosaurs.
State companies can also seek to use a compliant judiciary and tax police to put pressure on targets. One leading businessman says some bureaucrats see themselves as "Robin Hoods" taking assets from private "fat cats". "This is worse than in the mid-1990s, when businessmen paid courts to make particular decisions," he says. "At that time, everyone knew that what they were doing was bad. Now, judges think that by giving preference to state interests in a dispute, they are doing the right thing." There is also the danger of well-connected state managers winning favours for their businesses in a way that distorts competition. The leading Russian businessman warns that the state's growing role "kills initiative".
"A businessman who can't rely on state orders comes up with something the market needs," this businessman says. "But if the state starts handing out orders and money, people start thinking in terms of lobbying their interest in this or that government project. This requires not entrepreneurial skills but lobbying skills."
State companies may simply attempt to cherry-pick attractive private assets. One example is the pursuit of VSMPO-Avisma, the privately held titanium company, by Rosoboronexport, a state arms export agency headed by Sergei Chemezov, another long-time Putin friend. The same group last year took control of Avtovaz, the Lada car maker, and is emerging as a prime mover in the new state capitalism.
The Russian Union of Industrialists and Entrepreneurs, a lobby group, has raised the alarm about the government's failure to protect property rights. In April it published research that concluded Russia's economic model had been most favourable for investment in 2002 and 2003, before state capitalism started to emerge. Had the climate been maintained, it added, a real investment boom would have boosted industrial output and the economy could have grown at nearly twice last year's 6.4 per cent. Even ministers have weighed in. German Gref, the liberal economy minister, recently warned that the sheer number of deals meant the government could not "keep track of state-controlled firms?.?.?.?as they grab market assets".
But is this asset grab the result of ideology - that state control is best - or attempts by officials to line their pockets? Mr Putin himself has denied that senior officials running state businesses are enriching themselves. Supporters say he put trusted allies into state companies partly to clamp down on corruption - notably Mr Miller, who has reclaimed $1bn of Gazprom assets spirited out of the company's control by Yeltsin-era management.
Yegor Gaidar, the former prime minister who masterminded Russia's post-communist economic reforms, says state control tends to breed corruption. "When you are the owner, you don't cheat the company," he says. "But when it isn't your money but the state's money, being a manager you suddenly find you have a lot of good friends and relatives who could benefit from this money."
Some observers say the process could go further: state managers could become owners through flotations or partial privatisations that would give them the chance to buy shares.
Most analysts agree Mr Putin was right to break the influence of the 1990s-era oligarchs, which was distorting competition and deforming the development of Russian capitalism. Yet rather than separating political and business interests in a stable system governed by the rule of law, he has created a new class of politically connected business people.
Russia risks becoming locked in a vicious circle of property redistribution and mutating oligarchies. To ensure they do not lose their own assets, those who have gained under Mr Putin will be prepared to use every resource at their disposal to ensure the election of his chosen successor in 2008.