How are deals originated & banks chosen?

It is a combination of expertise, which mouth needs to be fed, and ensuring the company has multiple banks lined up if it needs to (ie, relationship management). After 2008 lots off companies realized that they can't always rely on a single bank to supply credit in a downturn. This means they need multiple banks to form a bank group so they have multiple relationship banks (big full service banks with large balance sheets) to bank them simultaneously. Banks make very little money off of balance sheet lending, so they demand that clients give them capital markets takes (issuing debt, equity, financing their acquisitions, and providing M&A advice). This is why so many shitty banks have ECM and DCM teams these days. They are able to because they force their clients to use their services. 

Now you're probably wondering, ok, what about the boutiques which have basically no balance sheet? This is more of the advisory stuff where expertise comes into play. Expertise includes having connections to find a buyer when one is needed or a seller when one is needed. Additionally, sometimes the big banks are conflicted and can't assist (maybe they already bank one of the parties, or maybe in a restructuring, they are a lender to the BK company etc). Now why doesn't KKR just choose one elite boutique and call it a day? For one, no one EB is the best at any everything. Sponsors also have to interact with their target's advisor when they are trying to acquire. Their target's advisor may occasionally be their advisor. When multiple sponsors make offers to a target, with different terms and such, they want to have a good relationship with that sell-side advisor so their bid "gets to the top of the pile," so to speak. Obviously, if one bid is way at the top, that firm is going to get it. But, what I the bids are pretty much the same, but have different terms and conditions. If that sell-side advisor can count on you for future buy-side mandates, maybe they'll nudge their client in your direction. All these things play a role in different banks getting deals completed. Sponsors like lots of competent M&A advisors hanging around. This creates competition and compresses fees.