until a couple of years ago there was only one telephone provider. Uno.
Then, the Danish
phone market was liberalized and other companies (especially cellphone providers) swarmed
the country, but the physical phonelines are still owned by the former monopoly (recently changed name from Tele Danmark to TDC) in telecommunications. Be afraid. Be very afraid.
In order to get DSL in Denmark (ADSL actually, since that's the only variant used here) you have to either sell out and buy the service from TDC or try your luck;
In order to use any other provider you need not one but two phone lines out of your house installed (one for ADSL and the other for normal phone services)for some obscure reason that is vaguely explained by the untrustworthiness of the other companies' equipment.
Furthermore you need a TDC technician to actually check out whether or not your line is usable for ADSL.
Needless to say, sadly, they're being complete bastards about it and take their time doing this if it's for other companies and always have slightly elevated prices because of peoples tendency to chose the comfortable solution(oh, and the fact that not everybody has two phone lines installed per default and that it's outrageously expensive to lay them).