Caviat: I am not a lawyer; I am not your lawyer, barrister, solicitor, etc. I've never even been to Britain.
A quick google search suggests that your stated understanding of "overreaching works in sale of trust property" is incorrect (which may be a stumbling block). It appears that what is "over reached" is an occupier's (e.g. a tenant) overriding interest. Also to explain in the context of overriding interest:
- Normally, when one purchases land "unencumbered", one has all the property rights associated with that land.
- It is possible to distribute interests in the land to other parties (e.g. tenancy, or granting a right to use a portion of a stream on a given property for fishing).
- It is possible to register such interests in the Land Registry; if such interests are not registered, they "die with the grantor" or at least with their interest.
- There are certain interests that do not need to be registered with parcel in the Land Registry. These are the "overriding" interests, that "override" the rule that interests need to be registered to survive transference.
- The overreaching doctrine allows distributions or sales from trusts to "overreach" certain overriding interests into the real property. The overreaching doctrine therefore is a means of "quieting" a title to real property.
With that in mind:
- "trustee lawfully distributes trust property to beneficiaries of the trust"
Imagine scenario #1, a trust exclusively of money. The trustee
divides the money appropriately, and gives (distributes) it to the
beneficiaries. Straightforward.
Now, imagine scenario #2, a trust exclusively of property (clothes,
jewelry, automobiles, other goods and yes, real estate). It is quite
possibly for a trustee to sell such goods on the open market, and
distribute the proceeds to the beneficiaries of the trust. Likewise,
scenario #3, in which the trust contains property (it need not be of
exclusive composition). It is possible, rather than to sell property
and distribute money, to distribute other property directly to
beneficiaries, e.g. one's parents die, and one inherits their house
(generally that would be through a will not a trust, but the two instruments are similar).
Thus, "The overreaching doctrine is not confined to sale of trust property; it will also apply where the trustee lawfully distributes trust property to beneficiaries of the trust." can be read as "regardless of whether the trustee sells the property to a third party, or distributes it to the beneficiary, the overreaching doctrine applies".
- Those beneficiaries will receive the property absolutely and, since there is no exchange product, there will be no replacement property in which the remaining beneficiaries have an equitable proprietary interest [emphasis mine].
Imagine a scenario where a trust grants 3 beneficiaries (let's call them Alice, Bob and Charlie) equal stakes in say, a house. One beneficiary wishes to own the house outright ( Alice), and so a fair price for the house is determined (3 pounds, or 3 million pounds) and the first beneficiary pays it to the trust, as in scenario#2 above. However, generally what what happens is that the first beneficiary would only actually pay only a fraction of the price, divided proportionally among the other ("remaining") beneficiaries. E.g. the house is determined to be valued at 3/3million pounds, so Alice pays 2/2million pounds to be split between Bob and Charlie. The money is the "replacement property".
My reading of the bolded section is that it is clarifying that in the case where the real property is distributed, rather than sold. E.g. Imagine a trust with a 1 million pound house, and 2 million pounds in "cash" money; the trust could distribute the house to Alice, and a million pounds each to Bob and Charlie.
#3. For the picture, I will leave that to those with artistic or graphical skills.