Currently the Deutsche Telecom is still controlled by the German government. The government owns 30.9 % of the company (1) and with the Regulierungsbehörde (english: regulation administration) it controls the telecommunication market, as it isn't really a market, at least for normal telephone services. The Telekom's competitors have round about 1.5 % market share (2) (actually the Telekom has more lines than there are households in Germany). Other telecommunication sectors aren't that influenced by the Telekom, but it still is a major player in them. The mobile phone market in Germany is shared by four big companies: D1 (Telekom), D2(Vodaphone), E1 (E-Plus) and E2(Viag Intercom), but the D1 net is the biggest one with 19 million customers (3) (of 48 million in total (2)). The Telekom is the former owner of the German cable net, too. But it had to sell it, because controlling the normal telephone service and cable service made it nearly impossible for other companies to provide high speed internet access and because the Telekom neglected cable service as it could have been a rival for its DSL service TDSL. The Telekom sold cable service to three different companies: Callahan, Liberty Media and E-Kabel (4).

T-Online, Germany's biggest ISP, is a subsidiary of the Telekom and provides Internet access for 6.5 million Germans (3). Though most of these are modem or ISDN users, the Telekom is also the biggest high speed internet connection provider in Germany with 620000 customers (3, but numbers are outdated) via DSL.

The Telekom (short for Deutsche Telekom Aktien Gesellschaft (DTAG)) was founded 1989 as the German post service got reformed and partly privatized (still in progress). In the beginning the company was called "Deutsche Bundespost Telekom" but since 1.1.1995 it is a Aktiengesellschaft. Since November 1996 the Telekom is a member of the DAX and a big part of their stocks are in free float.

But the Telekom is not only a big player on the German market, but also one of the strongest telecommunication companies europe- and world-wide owning companies(sometimes partly, but sadly I did not find any information about the correct numbers) like Voicestream, Powertel, One 2 One or Ya.com and having branches in most European countries.
One of the more amusing facts: The Telekom is one of the 6 "companies" (mostly more than one company formed a syndicate), which bought the highly overpriced German UMTS licences during an auction for 16.5 billion DM from the German government. So the government buys for its own licences. That's what happens when mixing free market with planned econonmy.

sources: (1): http://www.bundesfinanzministerium.de/Anlage4836/Privatisierung-von-Bundesunternehmen.pdf
(2): http://www.regtp.de/service/start/fs_02.html
(3): http://www.telekom.de/untern/inv_relations/gesch_zahlen/statistik/index.htm
(4): http://www.digitv.de/kabel/kabelvekauf.shtml
Der Brockhaus - In fünfzehn Bänden, Brockhaus GmBH, Leipzig-Mannheim, 1997