The width of your back is determined but the size of the latissimus dorsi and the teres major. These are the muscles that are most prominent in the rear lat spread pose.You always want to build a bigger back. But keep in mind that your lats are displayed with front poses like the front double biceps pose, front lat spread, and abdominals and thighs pose.
The exercises that most effectively target these muscles are lat pull downs with a wide overhanded grip. This will hit the upper portion of the lats as well as the teres. You can modify this exercise by using a narrow underhand grip. To hit the lower portion of your lats I suggest doing bent-over bar rows with an underhanded grip. Just make sure you are at approximately a 30 angle from being completely upright. The final exercise I would suggest for this portion of your back would be pullovers either with cables or with a dumbbell.
Back thickness mostly depends on the size of your erector spinae, middle,lower, and upper trapezius, and posterior deltoid. The posterior deltoid really adds to back thickness front a side position because it makes your overall physique look thicker. You want to be building more muscle
Developing this part of your back is perhaps the easiest as far as number of exercises but also the most difficult due to amount of weight needed to stimulate the muscles. Some exercise suggestions for back thickness would be deadlifts, seated cable rows, t-bar rows, hyperextensions, and reverse flyes. For these exercises you really need to focus on high poundage repetitions using compound movements. Compound movements are those which involve numerous muscles in order to balance and support the body during the movement.