What sits in the book is legally firm, and the rule measures that firmness in round lots. Under 17 CFR 242.600(b)(86), "Quotation means a bid or an offer", and (b)(16) defines a bid or offer as a price communicated by an exchange member or an association member to any broker, dealer or customer "at which it is willing to buy or sell one or more round lots of an NMS security, as either principal or agent, but shall not include indications of interest." Two things follow. A quotation carries an obligation to deal, at least for a round lot, which is why a book of quotations is worth more than a list of expressions of enthusiasm. And a soft signal of interest is not a quotation at all, so it does not belong in the picture. Note the vocabulary: the rules say "offer" where traders say "ask". They are the same side of the market.
Size is part of the quotation, and the rule supplies a default. Under (b)(87) the quotation size is the number of shares the quoting firm has specified it will deal for, and where it has not specified one, the size is "a normal unit of trading for that NMS security." So a quotation without a stated size is not sizeless; it defaults.
Ties across venues are broken by size, then time. The national best bid and offer, defined at (b)(60), is the best bid and best offer calculated and disseminated across the market, and the rule anticipates a dead heat: where two or more market centers transmit identical bids or offers, the winner is determined "first by size (giving the highest ranking to the bid or offer associated with the largest size), and then by time (giving the highest ranking to the bid or offer received first in time)." That is a small provision with a large consequence, because it means the venue that gets to be at the top of the national quote at an identical price is the one showing the most depth there.
What the consolidated feed carries today is the best quote, not the book. Under 17 CFR 242.603(b)(3), every exchange trading an NMS stock and the national securities association act jointly through national market system plans to disseminate "consolidated information, including a national best bid and national best offer and odd-lot information", and the single plan processor for each stock "must represent quotation sizes in such consolidated information in terms of the number of shares, rounded down to the nearest multiple of a round lot." Depth below the best bid and above the best offer is not in that stream at all; it comes from a venue's own proprietary feed. Regulation NMS does define the deeper picture, as a building block of the market-data regime the same rule is phasing in: "depth of book data", at (b)(31), means "all quotation sizes at each national securities exchange and on a facility of a national securities association at each of the next five prices at which there is a bid that is lower than the national best bid and offer that is higher than the national best offer", with the size at each of those prices attributed to the venue it came from. Five levels on each side, and no more.
Two processing rules make the public picture different from the book, and this is the part almost nothing explains. Both live in the definition of core data at (b)(26) and both bind the firms that consolidate and publish market data rather than the venues that hold the orders. First, sizes are truncated: those firms must represent the quotation sizes of the best bid and offer, the national best bid and offer, the protected quote, depth of book data and auction information "as the number of shares rounded down to the nearest multiple of a round lot." A firm bid for 149 shares on a stock with a 100-share round lot is published as 100. This is the rule already operating, because § 242.603(b)(3) imposes the same truncation on today's plan processor. Second, small orders are bundled: the best bid and offer, the national best bid and offer, the protected quote and depth of book data "shall include odd-lots that when aggregated are equal to or greater than a round lot; such aggregation shall occur across multiple prices and shall be disseminated at the least aggressive price of all such aggregated odd-lots." So a cluster of small orders at slightly different prices can enter the public quote as one line at the worst of those prices. The round lot that both rules turn on is itself price-tiered under Regulation NMS rather than a flat hundred shares, which is covered on the odd lot page.
The practical reading. A displayed book is a truthful but lossy summary. Real resting size is at least as large as the displayed size and can be materially larger; some of the interest sitting at better prices is published at worse ones; and the consolidated feed stops at the best quote, so any depth on the screen came from somewhere else. An investor sizing an order against what the screen shows is sizing it against a floor, not against the market. Whether a venue displays its book at all is a separate question again, and undisplayed venues have their own page.