I rooted my SE wt19i 4 times,if you are on 4.02.A.0.58 it easy to root,and after that update over air to newest firmware 4.02.A.0.62,don't update over PC Companion because root will be canceled.
But if you all ready on newest 62 firmware it's little complicated.
Then you need to flash to previous firmware 58 using flashtool and download from net 58 firmware,that's ftf format file.
After flashing google it "Sony Ericsson wt19i root toolkit" and download from NAW_32,that tool work every time on my phone,follow the instructions and you will root without problems.
If you have any question mail me.