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). Licences for Alternative Investment Funds Managers (AIFM) are granted to legal persons with their head office and registered office in Luxembourg (Directive 2011/61/EU).
"INTRODUCTORY PART: DEFINITIONS
Article 1. For the purposes of this Law: [...]
26. “UCITS” means undertaking for collective investment in transferable securities subject to Directive 2009/65/EC;
[...]
PART I: UCITS
Chapter 1 – General provisions and scope
Article 2. 
(1) This Part applies to all UCITS established in Luxembourg.
(2) For the purposes of this Law, and subject to Article 3, UCITS means an undertaking
- “with the sole object of collective investment in transferable securities and/or in other liquid financial assets referred to in Article 41(1)”6, of capital raised from the public and which operate on the principle of risk-spreading, and
- with units which are, at the request of holders, repurchased, directly or indirectly, out of this undertaking’s assets. Action taken by a UCITS to ensure that the stock exchange value of its units does not significantly vary from their net asset value shall be regarded as equivalent to any such repurchase.
[...]
Chapter 2 – Common funds in transferable securities
Article 17. 
(1) For each of the common funds that it manages, a management company shall ensure that a single depositary is appointed in accordance with the provisions of this Article and of Articles 18 to 22.
(2) The depositary shall either have its registered office in Luxembourg or be established in Luxembourg if its registered office is in another Member State.
(3) The depositary shall be a credit institution within the meaning of the Law of 5 April 1993 on the financial sector, as amended. [...]" (Law of 17 December 2010 relating to undertakings for collective investment, Mém. A239 of 24/12/2010; last amended by Law of 21 July 2021; Articles 1, 2 and 17 [unofficial translation])
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"Article 1. Definitions
For the purpose of this Law, the following definitions shall apply: [...]
(39) “Alternative Investment Funds (AIFs)”: collective investment undertakings, including investment compartments thereof, which:
(a) raise capital from a number of investors, with a view to investing it in accordance with a defined investment policy for the benefit of those investors; and
(b) do not require authorisation pursuant to Article 5 of Directive 2009/65/EC; [...]
(46) “Alternative Investment Fund Managers (AIFMs)”: legal persons whose regular business is managing one or more AIFs;
[...]
Article 6. Application for authorisation
(1) The taking up of the activity of AIFMs established in Luxembourg is subject to an authorisation by the CSSF.
[...]
Article 7. Conditions for granting authorisation
(1) The CSSF shall not grant authorisation to the AIFM established in Luxembourg unless the following conditions are met: [...]
(e) for each AIFM established in Luxembourg, the head office and the registered office of each AIFM are located in Luxembourg. [...]" (Law of 12 July 2013 on alternative investment fund managers, Mém. A119 of 15/07/2013; last amended by Law of 21 July 2021; Articles 1, 6 and 7 [unofficial translation])
Law of 17 December 2010 relating to undertakings for collective investment, Mém. A239 of 24/12/2010; last amended by Law of 21 July 2021; Articles 1, 2 and 17
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 undertakings for collective investment in transferable securities (UCITS), Article 23
Law of 12 July 2013 on alternative investment fund managers, Mém. A119 of 15/07/2013; last amended by Law of 21 July 2021; Articles 1, 6 and 7
Directive 2011/61/EU of the European Parliament and of the Council of 8 June 2011 on Alternative Investment Fund Managers and amending Directives 2003/41/EC and 2009/65/EC and Regulations (EC) No 1060/2009 and (EU) No 1095/2010
[<a href="https://legilux.public.lu/eli/etat/leg/loi/2010/12/17/n9/jo">Law</a>],[<a href="https://www.cssf.lu/wp-content/uploads/L_171210_UCI.pdf">Law_Eng</a>],[<a href="https://eur-lex.europa.eu/legal-content/EN/ALL/?uri=CELEX%3A32009L0065">Directive</a>],[<a href="https://legilux.public.lu/eli/etat/leg/loi/2013/07/12/n1/jo">Law</a>],[<a href="https://www.cssf.lu/wp-content/uploads/L_120713_AIFM_eng.pdf">Law_Eng</a>],[<a href="https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX%3A02011L0061-20190113">Directive</a>]