Initially began with an online application, it was one of the most challenging processes there is. The online tests (numerical and verbal) were pretty standard for those amongst big graduate recruiters. All I can say is practice practice practice. The pass threshold is 30%, I'd imagine a strong performance favours you later on though.
The telephone interview stage is where a lot of people fall. It's mostly competency based, although they will test your knowledge of why KPMG, PwC etc. I found the HR interview pleasant and friendly, this curtained helped keep me calm. Practice the STAR approach for this and you should be fine.
The immersive assessment centre is both tough and exciting. It consists of five tasks, a verbal re-test, virtual inbox exercise, report writing exercise, and two meetings (one client, one manager). Throughout eh day they tell you what competences they are looking for, which helps focus your attention. Also, just as a side note, you are able to provide feedback at the end of each task which is assessed. Make sure you talk about everything you would have done given more time etc as I think this has a very strong bearing. They don't expect you to be perfect in I time pressure, they just want to see how you work with certain situations.
Last but not least the partner interview was very friendly (although mine was very structured). Presentation followed by a lot of questions. Best advice is know KPMG inside and out. Services they offer, latest business news. This comes across well. My partner was great, I felt nervous at times but with the information he gathered during the interview he gave me a great insight into the areas which I may succeed in (even if I had failed).
All in all, good experience and great staff along the way.