I upped my pullup numbers from 12 pullups to 26 pullups in a couple of months by doing Latters as described by Pavel. In the first month I was greasing the groove and just knocking out 1/2/3 (=6) Pullups whenever I could until I reached a limit of a little bit more than just 50 Pullups. Kept up doing the same in the second month but increased the number of total reps until I was doing 100reps a day with ease.
Then I went on to 2/4/6 latters and worked myself in 2 weeks fom 50 reps a day to 100 reps a day. After getting the job doe with that I took a few days off and decided to knock out 100 Pullups in one workout in the best time possible. I managed to do 2/4/6 x 7 and 1/2/3 x2 + 4 pullups in 43 minutes. Then i just went on with increasing the total reps every day. Right know I can do 150+reps a day and manage 100 Pullups in 27 minutes! My all out and best ever was 26 Pullups in a row and I was even working out on my gymnastics/barstarz routine the day before.
By the way:
Do your pullups without the thumbs during training and get back to doing them with thumbs during your all out tries. You will fly through your reps
Another thing that I realised was that switching to thicker bars during training upped my results even more and even increased my forearm size.
If you are doing a max attempt try to hang on the bar with one arm and shake the other one for 5-10 seconds, then repeat with the other hand and keep going.
I can just recommend to play arround with Latters, they work with other max strength calisthenetics like one arm pushups and pullups as well.
The results? My Lats are finally starting to grow and I have added veins and seize to my arms.
+ My buddies in arm wrestling say I am literally crashing their hands lol