This one comes up time and time again, so let’s make a post with all of the available options and ideas currently available in the UK. Please add replies below with your experiences of ones you’ve used, which you prefer, and why.
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Intro
Propagation trays are a big expense and big decision to make when starting a tree nursery. Most nurseries will tend to stick to one type where possible to improve efficiency of space planning and handling, but it is well worth getting samples of a few different types before committing.
Of course, all of this only applies if you want to grow trees in cells. Tree nurseries were around before root trainers existed and grew directly in the soil in fields and in beds. Many commercial nurseries still operate this way and there is no doubt it involves less plastic (trays, polytunnels etc) but there are many factors to consider - perhaps one for another discussion topic?
Before we get into the list, it is worth pointing out if you’re reading this as someone just wanting to try growing a few trees for yourself, you absolutely do not need these specialist trays! Any reused pot will do, drinks cartons etc. Something with at least 10cm depth. These trays are for efficient use of space and uniformity in a tree nursery.
Sizes
Trays for trees tend to be at least 10cm deep and around 4-5cm diameter. They can be round or square, and tend to have vertical lines or ribs to direct roots downwards and discourage spiralling. They have a large open hole at the base to promote air pruning of the roots (the tray must be suspended with some airflow beneath for this to work).
Materials
The main differences in the trays and containers suggested below is their manufacturing methods. All are made from plastic, many of which will include a good amount of recycled content.
Vaccuum forming is a cheap way to make plant pots and root trainers. These tend to be thin plastic and flimsy. They will last several seasons if well looked after though.
Injection moulding is more expensive to setup and uses more material but results in a thick and sturdy tray that can withstand years of use and abuse.
Products
Products listed below are available to buy in the UK. Links to find out more or purchase are listed but we have no affiliation with these and ther may be other suppliers.
‘Book’ Rootrainers 
Book type Rootrainers are very common in nurseries. They comprise a folding ‘book’ rootrainer and tray that they go into. The deep rootrainer is 12cm deep and 175cc volume. A Tray holds 32 cells.
They are cheap. Easy to open and check root development. They fold away for storage
They are pretty flimsy thin plastic and tend to tear and break apart. However with care they will still last several seasons. Roots can often “bridge” cells and need snipping when opened.
Containerwise
Containerwise make a huge selection of different sized rigid plastic propagation trays. They have many different sizes that are suited to different trees and shrubs. 40H and 54Universal are great sizes.
Bombproof! These are VERY strong and will last a long time. There’s a multitude of sizes and styles to suit your setup.
Quite expensive - certainly a big investment if you are starting a new nursery. They can be bulky but the trays do stack well if the same size.
Proptek
Another high quality rigid tray.
I have no experience of these so waiting for someone else to write this section!
Other Root Trainer Trays
These are sold by various brands such as Nutleys, Muddy Hands etc. They are very thin vacuum formed plastic and not suited to repeated use in a tree nursery. Photo below for reference.
Any others? Please add them to the list or post a reply below. We’d also love to know your experience of those listed and your preferred sizes for different species.