The back isn't a muscle, it is made up of a group of muscles.
Pullups/Pulldowns with various grips build latisimus dorsi.
Rows of all kinds build trapezius.
Deadlift variations build erector spinae, glutes, hamstrings and trapezius.
Some will argue that there is an overlap. Well of course there is. You can't isolate a muscle however the idea is to stimulate one the best way possible.
A decent back routine would look something like this:
Trap Bar Deadlifts ramp up to a top set of 3-5
Weighted pullups 5 x 5-7
One Arm Dumbell Row 3 x10-12
Seated Cable Row 3 x 10 -12
Unlike most muscle groups the back can take a pounding so I would do any deadlift variation on a different day such as legs day.
Doing this can mean adding an extra lat exercise such as lat pull downs on back day.
Edit: I just read that you are bicep dominant. In that case you will get a lot out of pre exhaust training.
What this means is working your back first without arm involvement. Exercises that come to mind are straight arm push downs. Pullover machine if your gym has one would be excellent. Kyak rows is another that Christian Thibideau used to recommend.
The idea is to pre fatigue your lats and trapezuis so that when you do your pullups and rows you wont be feeling it in the biceps.
You wont be able to use as much weight but so what. Building muscle is about creating tension not how much weight you can lift.