What you will find is the most probably explanation of 1 share parcels appearing and disappearing... is the trading system called ITS that brokers use, and crossings.
From my understanding, a broker has to appear at the price level they want to cross at, and the ITS system places 1 share at the price they want to cross, so that they fulfill the market rule of "appearing" at that price.
Once they appear at that price and a crossing market exists (something like min. of 10 seconds of the bid and ask being one tick apart), then they can cross their shares.
At this stage, the shares are crossed, and the 1 share parcel is removed as it is not included in the crossing parcel.
If you look in the course of trades after a 1 share parcel appears and then disappears... you will almost 100% of the time see a trade with a reference of XT has gone through... a crossing.
Cheers,
the 1 share thing, page-12
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