Basically much of what is said above is correct (I am assuming we are talking about UK law, not US - US is a maverick in international copyright terms). A song combines two things, a literary work (the words) and a musical work (the melody). The first owner of each of those is the author (unless they are created in the course of employment in which case it is an employer) if the author is a "qualifying person" or if "first publication" take place in a "qualifying territory". A "qualifying person" is a citizen or subject or resident of a "qualifying territory". Almost everywhere is now a "qualifying territory", but prior to October 1957 the USA was not and there can be very very interesting issues about pre-1957 US works. Many were "simultaneously published" (which did create UK copyright) in the UK or Canada (a country that was party to a suitable convention) so did ahve UK copyright anyway, and almost all others will have come into UK copyright in 1988/9 when the USA joined the Berne Convention. NB the rules are different for films.

The owner of copyright may assign or license it in whole or in part, as to categories of acts, as to time, by geography, etc. This should be in writing but that is not an absolute rule.

Upon the death of the author, copyright subsists for a further 70 years and to 31 Dec (it used to be 50 and there are some interesting issues about revived copyrights). Existing assignments and licences will continue in effect subject to the proviso to sections 5(2) and 11(1) of the UK Copyright Act 1911.

Upon the death of the owner (or licensee) the relevant right will pass under their will or intestacy - via their "estate" which is administered by their executors or administrators - (subject as aforesaid). The estate is not a legal entity in its own right. If a company is the Owner or Licensee and is liquidated then unless the terms of the assignments or licences terminate the rights they may be sold by the liquidator. If they are not then when the company cases to exist and is struck off the register (for any reason) then the rights become "bona vacantia" (rights without an owner) and vest in teh proper authority, usually the Crown of the Duchy of Cornwall or the County Palatine of Lancaster) and will then be administered by the Official Receiver (the department of bona vacantia). US law differs and a company's rights vest per stirpes in the shareholders. There are different views about what rules apply if a US company ceases to exist owning a UK copyright or vice versa - do UK or US rules apply?

A licensing body (MCPS or PRS) will only administer rights if the rights owner/licensee is a member and will have rules that I do not know for when a member dies (or if a company ceases to exist).

If a rights owner is NOT a member of the MCPS or PRS then he administers the right not the MCPS or PRS.

And now the twist:

There can also be a copyright in an arrangement or adaptation of a work and a well-known performer of it MIGHT have been the owner of such a right. If he registered the work or that form of it with MCPS/PRS as "trad/arr" then he will get 100% of PRS or MCPS collections from the work - and if it was say "Named Composer/Arr Performer" then there should have been an agreement that specified the split.

I hope that helps.