1. Investopedia: Book Runner
The main underwriter or lead manager in the issuance of new equity, debt or securities instruments. In investment banking, the book runner is the underwriting firm that "runs," or who is in charge, of the books. A large, leveraged buyout could involve multiple companies, and the book runner works with the other participating firms. Typically, one company takes the responsibility of "running" or handling the books, and the book runner is listed first among the other underwriters participating in the issuance. More than one book runner can manage a security issuance, in which case the involved parties are called "joint book runners."
Also called managing underwriter or syndicate manager.
In investment banking, a syndicate is comprised of a group of underwriters who are responsible for placing a new equity, debt or security issue with investors. The book runner typically assigns parts of the new issue to other underwriting firms for placement, while keeping the largest part for itself. The book runner syndicates with other underwriting firms in order to reduce its risk in the issuance of the new equity, debt or security.
2. Campbell R. Harvey: Book runner (via Financial Dictionary)
The managing underwriter for a new issue. The book runner maintains the book of securities sold.
3. Farlex Financial Dictionary: Lead Arranger (via Financial Dictionary)
In investment banking, an underwriting firm that leads a syndicate. A syndicate is a group of underwriters responsible for placing a new issue of a security with investors. Every syndicate is a temporary arrangement. The lead arranger assigns parts of the new issue to other underwriters for placement and usually takes the largest part itself. It is also called a managing underwriter or a syndicate manager or, less formally, a book runner.
4. Bankopedia: Bookrunner
Bookrunner is a bank appointed to run the books during the execution phase of syndication or during the security issuance, with responsibility for issuing invitations, disseminating information to interested banks and informing both the borrower and the management group of underwriters of daily progress. In security issuance deals there is usually more than one bookrunner, and they are called joint bookrunners. However, if there is no further syndicate involved in the execution of the offering, the bank executing the deal is called the sole bookrunner.People came here searching for:
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5. Financial Times LEXICON: lead-left bookrunner
Lead-left bookrunner is the major bank within a bank syndicate, the group of banks who work together to underwrite a financial transaction, such as an initial public offering or a bond issue.
As syndicates have grown to include more banks, the title 'lead-left' is used to indicate the bank that has played the most important role in the transaction, and has been involved in the deal from an early stage.
The term evolved from the position of bank names in deal documentation – the most important bank being named first, in the upper left hand corner of a prospectus.
One cannot call a left-lead bookrunner the sole bookrunner if there were other bookrunners on the deal. Even if they were more junior in terms of role.
Defining the roles played within a syndicate is crucial in determining banks' league table positions. League tables are the main ways in which banks measure their performance against each other. Achieving a top ten position in a league table is also seen as an important tool for winning further client business.
Left leads have definitely played the most prominent role amongst a syndicate of banks. The term can apply to any type of transaction, be it bonds, equities or loans.
ExampleLeague table 'credit' is awarded commensurate with the importance of the role. Credit will be split equally among underwriters that are identified in a deal's prospectus as joint bookrunners or co-bookrunners, for example, while banks identified as 'left lead' receive more league table credit. 
6. WallStreetOasis.com: Lead Manager vs Bookrunner
(6.1) Being the lead manager in a deal means that you are structuring the deal. They don't want clients at other banks knowing this, but most of the profits from the deal can be gotten by what they call "the skim" (at least at my banks). Its basically the amount they can sell to the institutional public above the price they underwrote it for for the company. The lead manager makes all the decisions about price, timing, how to run the roadshow, what type of auction they will pursue, who gets stock, etc. The bookrunner is usually the lead manager but doesn't have to be. They are basically in charge of "keeping the book" which simply means keeping record of who bought shares for how much. Every bank wants to be the lead manager, because that means they get the best price for themselves and their customers, meaning fatter commissions.
Usually to get to the most customers there are as many as twelve other syndicate banks, who buy blocks of stock to sell to their clients for higher prices than they bought it for. But they are kind of along for the ride. ( ... )
(6.1.1) I am pretty sure this only applies to I-Grade deals these days. Pretty much every HY issue has been best efforts meaning the bookrunners (lead and one to 3 co-books) share the majority of the execution and diligence with several co-managers helping to syndicate. In a typical HY deal with 200 bps in fees, the bookrunner will split at least 150bps with the 4-5 other comanagers just getting a small piece of the 50 bps.( ... ... )
7. InvestmentBankingInsight.com: Lead Left Bookrunner
The “Lead Left” Bookrunner is the investment bank chosen by a client to lead a capital markets transaction and is usually identified as the upper-left hand bank listed on the offering document cover. Typically the Lead Left Bookrunner has been involved in the proposed deal from the onset and largely controls transaction details (roadshow and marketing process, updates with capital markets desk, drafting of offering documents, diligence sessions, etc) and generally gets a better economic position in the transaction and is likely to be selected for other deal functions (such as stabilization agent or structuring agent).
Why is being the Lead Left Bookrunner important? Being on the left is the most prestigious position for a bank to have on a transaction – the managing director who wins the deal gains status with other potential clients in the same sector who may consider a similar transaction at some point in the future. Winning enough deals can establish a bank as the de facto “expert” in that category of transaction for that sector. Consistently being the Lead Left Bookrunner indicates that a bank is very well plugged-in to an industry (or deal type – ie one bank may do a significant number of high yield bond deals in the media industry). The insights gleaned (both industry knowledge and deal execution experience) from leading deals is critically important in building and broadening client relationships for the senior bankers.
What does being “on the left” mean for the junior banking team? Put simply: more work. If one were just to calculate economic benefit per man-hour expended, being a non-Left Bookrunner would be much more financially lucrative than being on the left. Often the non-Left Bookrunners will participate in the initial organizational meeting and subsequent drafting and diligence sessions, but the Left Bookrunner will drive 99% of the marketing materials, financial documentation and quantitative analysis/modeling.