FAMILY COMPANIES COME in many guises. In a paper published last year Soumodip Sarkar, of the University of Evora, and two colleagues identified 200 different definitions. Some people use the term as a synonym for a small company, for others it means a closely held company. This special report will define family companies as those with families as either owners or managers or a combination of the two. They must involve more than one family member, and there has to be a succession, or a planned succession, from one generation to another. In a new book, “The Family Business Map”, Morten Bennedsen, of INSEAD, and Joseph Fan, of the Chinese University of Hong Kong, explain that this basic model comes in four main flavours.

In a classical family company the family exercises both ownership and control</strong>, as exemplified by members of the Hénokiens Association, an international club of 44 family businesses that combine family ownership and management and are at least 200 years old. They include 14 Italian companies, 12 French, five Japanese, four German, three Swiss, one British and one Austrian. The British have gone one better with a Tercentenarian Club of companies, owned and controlled by the same family for over 300 years.

As firms get bigger, this combination of ownership and control becomes harder to maintain, but a few manage to hold on to both. Lakshmi Mittal, scion of an Indian steel dynasty, owns 41% of the shares of Arcelor Mittal, the world’s largest steelmaker, and acts as both chairman and CEO. Charles and David Koch between them own 84% of the shares of Koch Industries, a company with revenues of $115 billion. Charles Koch is the CEO and David his loyal lieutenant.

In the second model, the family owns a controlling stake in the company but hands over the running of it to professional managers. The Walton family owns around half of Walmart but does not run it on a day-to-day basis. Passive ownership can be risky for families. The Cadburys retreated from direct management of their chocolate empire and progressively diluted their family control, so when Kraft, a giant American food company, made a hostile bid for the company in 2010, all they could do was protest.

Some families seize their patrimony back from professional managers</strong>. Li & Fung, a Hong Kong-based trading group, saw the family’s control slip away after the company was listed on the Hong Kong stockmarket in 1974. But in the mid-1980s William and Victor Fung reasserted family control by borrowing to buy out other owners and then relisting the company on the stockmarket in 1992.

Third, and more surprising, in some family companies the family retains very little ownership but continues to play a managerial role. This model is fairly common in Japan.</strong> The Toyodas and Suzukis have only small shareholdings in the companies that bear their names, but Suzukis have managed the company for generations. Toyota appointed Akio Toyoda CEO and president in 2009 when the company had been forced to recall 4.2m cars after a safety scare. The eight families that in 1917 founded Kikkoman, a soy-sauce company, own just 20% of it now, but the post of CEO continues to rotate among them.

In a fourth type of family firm the family turns itself into a venture-capital fund to give its younger members a start in life.</strong> The Mulliez family owns one of France’s leading retail groups, Auchan, and younger members have used family money to found many other companies, including Decathlon (sports), Pizza Pai and Flunch (catering), Leroy Merlin (do-it-yourself) and Boulanger (electrical appliances). These businesses are all owned by a holding company, Cimovam, that employs 366,000 people.

Many family companies are hybrids, alternating between giving managerial roles to family members and bringing in hired guns.</strong> Barings flip-flopped between family and non-family CEOs before the bank went under in 1995. Since Henry Ford died in 1947, three members of his family have been CEOs.

The prevalence of the hybrid form argues against the idea that families tend to move from being owner-managers to passive shareholders. That seems to have been the dominant model in the Anglo-Saxon world, but not elsewhere. Julian Franks of the London Business School and his colleagues studied more than 30,000 firms across Europe and found that older firms in France, Germany and Italy are in fact more likely to be family-controlled than younger ones.