I understand what the 16 compartments are. What I don't yet understand is why the "dominant" compartment is something other than the fastest or slowest compartment.
The different compartments have varying times to absorb and release nitrogen. Specifically for release, they use a 'half-time' - the period of time that it takes for 50% of the starting nitrogen to be released.
When any given compartment reaches saturation, you are in 'deco'. That can happen quickly with the fastest compartments, but those compartments will also clear (sufficiently desaturate) during the course of a normal ascent (at pre-determined max ascent speed). This is why divers are recommended to not exceed a certain speed. PADI say 18m/60ft per minute. Most dive computers use 10m/32ft per minute.
The saturation level of a set compartment is described by its '
M-Value'. The
Max amount of saturation that can occur (relative to ambient/surrounding pressure) without undue risk of bubbles forming.
This is why some divers will argue that there is technically no such thing as a 'no-deco' dive. In reality, you always complete deco, but recreational 'no-deco' limits just keep your deco obligation below the level that would permit sufficient desaturation during a controlled ascent. Thus, you can see the critical importance of controlled ascents
When a diver is sufficiently saturated that their slower compartments become saturated, then those tissues may not clear at a speed that allows sufficient nitrogen release to occur during a controlled ascent alone. Extra 'stops' are needed during the ascent to provide more time for nitrogen release. These are 'deco stops'.
When a diver has saturated multiple compartments, they begin to ascend and, in that process, actually clear their fast tissues. However, their slower tissue compartments are still not cleared. Thus, the slower compartments are now 'controlling' the dive.
Repetitive Dives. This is especially relevant if multiple daily/repetitive dives are conducted, as slower tissues retain nitrogen from one dive to another (called 'residual nitrogen' on the tables). After a couple of dives, these slower compartments can become heavily loaded, even whilst the faster tissues are not. Thus, medium-slow tissues can be the controlling factor from the start of the (repetitive) dive. This is one reason why a diver should never assume that some small deco will 'disappear' on ascent. After several dives, you may well be controlled by slower tissues that won't desaturate at a speed faster than your ascent rate.
Multi-Day Dives. When you start conducting intensive multi-day repetitive diving; for instance 4-5 dives per day on a liveaboard trip, then your very slowest compartments can soon become the controlling tissues. Day-after-day, you leave the water with slightly increased slow tissue saturation. Whilst you continue to desaturate overnight, the slowest tissues won't completely clear, so you'll be topping them up the next day, and the next. After a few days diving, you'll be waking up in the morning still heavily saturated in the slowest compartments and taking that nitrogen back into the water with you.
I remember graphing my dive computer profiles after my first intensive diving trip to Thailand, diving heavily very day for 2 weeks, to learn that I was entering the water in the morning with my slowest compartment already at 85% saturation. I would add maybe 5% per dive, lose a marginal amount in the surface interval and then lose about 5% overnight - a rough gain of 10% per day. As you can see, in my second week of diving, the slowest tissues were very much 'controlling' the dives. In this case, any over-stay beyond the computer supplied NDL would have rapidly generated long deco stops (to the point of being nearly exponential).
Residual nitrogen tracking. This reality differs from the PADI tables, that lead you to believe you are 'nitrogen free' after a surface interval of >6-8 hours. Those tables weren't meant for multiple deep dives or intensive multi-day diving. However, natural conservatism inherent with the tables (assuming some element of multi-level diving) and tables rules (don't repetitively dive below 30m) can help this becoming an actual health risk. Your dive computer WILL track that accurately though.