Samsung s4
American M919
T Mobile root
firmware 4.4.4
Test on my own cellphone that why share it, it works 100 per fine no crash etc i do it to remove T Mobile and extra apps from my cellphone , so here is the simple trick Download this packageextract it on any where install drivers if your on some old windows, open odin click ap button collect cf file from same folder after this plug you device in download mode vol down power menu and power at same time you ill see logo click vol up for download now connect the cable see following of google it.
now pres start from odin let it process after this it ill auto goto recovery let it do its job be patience it will show pirate android logo to tells you its rooting after this restart now done you ill see super user in menu ...,