Each hivefleet is made up off millions of individual bioships

• White Dwarf:
"The Tyranids have travelled to the Imperium in a hive fleet consisting of a great dark swarm of millions of individual spacecraft. Each spacecraft is a gigantic living beast, a creature fashioned from organic tissue by means of sophisticated genetic manipulation..."

• Outer Dark:

"They are breaking to attack us,’ Tyberos said, his helmeted head swinging back and forth as he surveyed the data charts mapping out as close an approximation of the swarm’s formation as possible. Te Kahurangi realised he was right – a solid wedge of red, representing perhaps as many as a hundred major void-born organisms, was driving ahead of the ponderous mass that constituted the main part of the fleet. Even now yet more bio-ships were entering the sensorium range of the Carcharodons vessels, a seemingly endless procession of larger alien creatures. Te Kahurangi feared that even given the size of the swarm that had arrived so far – over a million organisms – they were viewing but a fraction of the primary fleet, the vanguard of a force that, when massed together, would be large enough to swallow up the greater part of the Segmentum Solar. The sheer scale was almost incomprehensible."

• Shield of Baal [Exterminatus]

"Numbering millions of bioships and lesser organism, the alien tendril divided as it sailed in system, heading to each of the inhabited worlds...

It was a hive fleet of almost unimaginable size, easily over a million void-faring organism and who knew how many trillion weapon -beast already spewed forth onto the Cryptan planets...

Anrakyr knew, as did the Dante, that even combined the Blood Angels and Necron fleets could not destroy the Tyranids; the void was thick with millions of bio-ships."

• Warhammer 40,000 Rulebook:

"Thus far, the Imperium has been struck by what they gather to be no less than nine distinct Hive Fleets. Each one of these living armadas is made up of millions of many-tendrilled spacecraft and on board each ship are millions of creatures ready for planetary invasion. The Magos Biologis of the Imperium has thus far categorized the separate forces, noting the defining characteristics that each of the self-sufficient Hive Fleet exhibits, the creatures it evolves and the tactics it employs during attacks Differing Hive Fleets seemingly have their own agenda and have sometimes competed with each other for food, occasionally even clashing with each other over a particularly bio-rich planet.

Unbeknownst to the Imperium, the threat is of an even greater magnitude, for the bulk of the Tyranids have not yet reached the Imperium's galaxy, their masses still strewn out across the void. So immeasurably large is the invasion fleet that its furthest stretched tentacles alone have entered the Imperium's space. Each of the identified Hive Fleets is but a splinter of that single monstrous host, the Hive Mind. What horrors await, only time will tell."