In the last months I've been watching and transcribing some dozens of Unitarian Universalist ordination prayers/invocations and laying on of hands, and also I've found other descriptive material
My research is not 'scientific', because I started searching specifically Christian Unitarian ordination prayer and then I expanded my accumulation of data.
And I noticed a phenomena: the cohabitation of two different theologies and practices: the congreational and the successionist.
The first one could be called rightly the 'congregational perspective': it consider the ordination mainly as an 'election', the choice of a congregation to recognize a person as a minister. As Susan LaMar put bluntly is his landmark article, the UU traditions stem from the congregational tradition, that denied the doctrine of apostolic succession in a favor of a democratic one centered on recognition of character and election to service by a community.
This theory often border with who consider ordination only as a 'union card' that permit the wider UU community to recognize that a person is apt to act as a 'teacher', having acquired necessary knowledge.
Ritually, it manifest in declaration before the laying of hands or the ordination declaration as 'The authority to confer ordination lies wholly within each congregation and not within any hierarchical power structure [...] congregational communities come together to recognize one among us who has answered the call to ministry as their life's work' ( Ordination of Rev. Emma L. Peterson, April 2, 2023) or a more common or generic 'the authority to ordain a minister rests solely with the congregation' (taken from the UUA bylaws).
There are also explicit affermations during ordination service that deny anything similar to 'apostolic succession': for example rev. Lavanhar in the ordination of Ren Pasco (May 22, 2021) said:
In the years past, the laying on of the hands was like apostolic succession: someone who laid hands on Saint Peter who was laid hands on Jesus (sic) and it went down through the line; in our tradition, we all are laying hands on you [...]
In contrast to all this affirmation, mention to ministerial succession and continuity pop up often: some example could be the introduction to the laying on of ands by the rev John Buherens (former UUA president) at the ordination of Lyssa Jenkens
You can feel the weight of your colleagues. You stand upon the shoulders of many generations of progressive ministers who have given their lives and their hearts to bring humanity out of its darkness and into its possibilities. Feel this. Feel this history of your colleagues, as you are about to enter this sacred, sacred journey of ministry.
and probably the fact that in this service the ministers were the first to lay hands and the the others through them only reinforced the sense of 'ministerial continuity'.