A depository of an  undertaking  for  collective  investment  in  transferable securities (UCITS) must either have its registered office in the same EU country as that of the undertaking or be established in  the  EU  country  if  its  registered  office  is  in  another  EU country (Directive 85/611/EEC).

Companies that manage alternative investment funds must have a permit from the Danish Financial Supervisory Authority if the assets in the alternative investment funds that the company manages exceed certain value thresholds. As a general rule for obtaining a permit, the company's head office and registered domicile must be in Denmark (Directive 2011/61/EU).
"§ 2. 
For the purposes of this Act:
[…]
11) Custodian company: A bank with a registered office in this country or a branch located in this country of a similar foreign credit institution with a registered office in another country within the European Union or in a country with which the Union has entered into a financial agreement territory, and depositaries referred to in Article 2 (2). 1 (a) of Directive 2009/65 / EC of 13 July 2009 on the coordination of laws, regulations and administrative provisions relating to undertakings for collective investment in transferable securities (UCITS) for UCITS domiciled in other EU or EEA countries that have been transferred
(a) all the financial assets of a UCITS; and
(b) the tasks set out in Sections 106-107 (b) of the Financial Business Act or Chapter IV of Directive 2009/65 / EC of the European Parliament and of the Council of 13 July 2009 on the coordination of laws, regulations and administrative provisions relating to certain collective funds; investment in securities (UCITS), as amended by Directive 2014/91 / EU of the European Parliament and of the Council of 23 July 2014 amending Directive 2009/65 / EC on the coordination of laws, regulations and administrative provisions relating to collective investment undertakings in securities ( UCITS) as regards depositary functions, remuneration policies and sanctions.
[...]"
(Act on Investment Associations (No. 1718 of 27/11/2020), last amended by Act no. 1163 of 08/06/2021, § 2 (11) [google translation])

******

"§ 1. This Act applies to
1) managers of alternative investment funds that have registered their domicile in Denmark,
2) managers of alternative investment funds which have their registered office in a third country and which have Denmark as their analogue country,
3) alternative investment funds established in Denmark and which are not covered by an agreement with a manager who is licensed or registered as a manager, on the management of the fund, and
4) alternative investment funds which are from a third country and which are not covered by an agreement with a manager who is licensed or registered as a manager, on the management of the fund, which has Denmark as its analogue country.
[...]
33) Analogue country: a country within the European Union or a country with which the Union has concluded an agreement for the financial area, as determined in accordance with Chapter 17th
[...]

§ 5. 
Companies that manage alternative investment funds must have a permit to manage alternative investment funds, cf. § 11, subsection. 3, or be registered with the Danish Financial Supervisory Authority, cf. section 9, subsection 1.
[...]

§ 6. 
Companies that manage one or more alternative investment funds must have a permit from the Danish Financial Supervisory Authority if the assets in the alternative investment funds that the company manages in total exceed a value corresponding to
1) 100 million euro or
2) 500 mio. provided that the company exclusively manages alternative investment funds that have not leveraged their investments and no investors in the funds are entitled to be redeemed for a period of at least 5 years after the date of the initial investment in each of the funds.
[...]

§ 7. Managers of alternative investment funds with a license who are registered in Denmark must be legal persons covered by the Companies Act.
PCS. 2. Managers of alternative investment funds registered in a third country which has Denmark as an analogue country must be limited liability companies.
PCS. 3. Stk. Paragraphs 1 and 2 shall not apply if the manager is an alternative investment fund that is self-managing.

§ 11. 
Companies that exceed those in § 6, para. 1, must apply for permission to manage alternative investment funds with the Danish Financial Supervisory Authority.
[...]
PCS. 3. The Danish Financial Supervisory Authority grants a company permission to manage alternative investment funds when the company is able to meet the conditions in this Act and when
[...]
5) the company's head office and registered domicile are in Denmark, unless the company is covered by section 1, subsection 1, No. 2 or 4,
[...]"
(Act on Managers of Alternative Investment Funds (No. 1047 of 14/10/2019), last amended by Act No. 1163 of 08/06/2021, §§ 1, 5, 6, 7 and 11 [google translation])
Act on Investment Associations (No. 1718 of 27/11/2020), last amended by Act no. 1163 of 08/06/2021, § 2 (11)
Act on Managers of Alternative Investment Funds (No. 1047 of 14/10/2019), last amended by Act No. 1163 of 08/06/2021, §§ 1, 5, 6, 7 and 11
[<a href="https://www.retsinformation.dk/eli/lta/2020/1718">Act on Investment Associations</a>],[<a href="https://www.retsinformation.dk/eli/lta/2019/1047">Act on Managers of Alternative Investment Funds</a>]