Just completed an internship at JPMAM - great firm, and they have roles on all sorts of desks - I was on Equities, and there were some other on Fixed Income, Real Estate, Investment Trusts, Ops, Risk and Finance. Applications are fairly competitive, just because there are only a few spots each year (our intern class was just 20-strong), and there are less AM internships going in the industry as a whole. I didn't have any formal experience at banks either, though I had enough other work experience (Consultancy, Law, Mathematical Research, and also working in the College Bar alongside studying) and demonstrable interest in the markets that it was alright. Definitely don't assume that you deserve anything - being smart is of course useful, but if you can't interact properly with your interviewers, or seem enthused by the role in front of you, you've got no chance.