During muscle hypertrophy induced by strength training, there are at least two separate processes which occur that increase muscle size and strength :
- Increased rates of muscle protein synthesis which creates more contractile proteins
- Myonuclear accretion / addition, i.e. increase in the number of myonuclei within the muscle fibers (donated by myosatellite cells) 
It is well established that the following factors affect the rate of muscle protein synthesis :
- Training volume
- Hormones (testosterone / anabolic steroids)
- Sleep / stress levels
However, it seems that there is less research around which factors affect the rate of myonuclear addition.
For example, we know that during a cutting phase, muscle protein synthesis is reduced even in the presence of sufficient training volume because nutrition is impaired.
Assuming adequate training volume, does the impaired nutrition during a cutting phase also reduce the rate of myonuclear addition? It seems logical, but it is a completely separate process to muscle protein synthesis so it would not be safe to assume this is the case.
Which other factors affect the rate of myonuclear addition?
1: Mechanisms regulating skeletal muscle growth and atrophy
2: Role of satellite cells in muscle growth and maintenance of muscle mass
3: Muscle protein synthesis in response to nutrition and exercise