Word: Inosculation

Inosculation

To unite (as of blood vessels, nerve fibres, or ducts) by small openings.
The opening of two vessels of an animal body, or of a vegetable, into each other.
To unite so as to be continuous; blend.

It is applied anatomically especially to blood vessels and in botany to the growing together of the trunks/branches of separate trees (as shown).

Needless to say the word is derived from In plus the Latin ōsculāre (having a mouth). The first usage is recorded by the OED as being from 1673.