What criteria are you using to gauge whther or not your lats are big or not relative to the rest of your physique? They may not be very thick or very wide, but they could still be strong. What are your stats (height and weight)? Can you do at least 10 pull ups? Unless you weigh more than 275 lbs. or so, you should be able do to at least 10 or your back is relatively weak.
I personally don't like t-bar rows or barbell rows. If you look at the movement, you will see most people cannot bend over far enough when doing barbell rows (the cannot bend over to a 90 degree angle and still row without falling on their face) to get a range of motion of more than 8 or 10 inches. If you look at the classic pull-up or chin-up you will get a much better range of motion in the movement (especially if you come almost all the way to full extension, and go all the way up to where the middle of your face is even with the bar). Also for a guy like me who can do 8 strict neutral grip pull-ups hanging a 90 lb. dumbbell from my waist (I am 5' 9", 167 lbs.) and one arm dumbbell rows with a 125 lb. dumbbell, bent rows would do no good for me. I would have to use 225 lbs. or more and I could not bend over and hold that much weight for a set of 8 to 10 without throwing out my low back. You should focus on core back movements (pull-ups, dumbbell rows - t-bar rows if that is what you like).
Whether your lats are wide or thick has nothing to do with the type of back training you do. Some ignorant people think that the wider your grip on pull-ups then the wider your back will grow. This is BS as Charles Poliquin has has stated. When doing a movement like a pull-up (regardless of width of grip) how can you flex the 'outer' part of your lat vs. the 'inner' part of your lat or vice versa? The answer is that you cannot. The same applies for the 'logic' of growing a peak in your biceps. You either are genetically predisposed to develop a peak or you are not. People also talk of the 'inner' and /outer' chest. There is not such thing there either. The pectoralis major has only one point of insertion for the tendon. Once again you cannot flex the inner chest without flexing the outer chest since they are all the same muscle anatomically. There is nothing you can do about it if it is not in genes. Change up your program and incorporate some new/different exercises into your routine.