Q:

Sci-fi book with a generational spaceship traveling the interstellar void

Spaceship is gigantic.  Most of the passengers don’t even realize that it’s a spaceship and the Author describes the world in great - captivating - detail.  The ship has forests, lakes and generally presents as a planet.  There are various levels and there is indeed a crew. 
The passengers are humans for the most part.
Muddled recollection that it uses Micro blackholes for propulsion.  It comes under siege.  The protagonist, a young girl aspiring to become the captain is the one that must gather resources – personnel and material – to help save the ship. The girl is an apprentice in engineering (or somewhere in the crew).
The ship is chased by planetesimals.  The ship is wounded by repeated attacks but it must get somewhere to find safe harbor.
Will add more details as and when I able to recollect.
Not too old.  Paperback.  Released in 2000s, I would reckon.  Might have been borrowed from my library around 2013.  The front cover has planets / depicts the chase (I think).
Never finished the book so can’t really say much about how it ends.
Please help find the book.

A:

Look like my wild guess was correct. OP confirmed that they were looking for the Great Ship series by Robert Reed:

In the distant future, an enormous ship larger than many worlds is
  discovered streaking towards the Milky Way at a third the speed of
  light. The near-immortal, TransHuman descendants of humanity are the
  first set foot on the enormous ship, and the first to claim it. The
  ancient reactors are warmed up, and life is nurtured inside the
  millions of enormous caverns inside the ship's hull. A burst from the
  moon-sized engines catapults the ship around a brown dwarf, setting it
  into the galactic plane, where humanity sells berths on the Great Ship
  in exchange for worlds, information, and technology. The nearly
  indestructible hyperfiber hull makes the Great Ship Nigh Invulnerable,
  a very desirable feature to the nearly immortal, fantastically rich
  sentient entities in the galaxy, who desire something safer than a
  planet to reside on. Technology, colonization rights, pledges of
  assistance, and information is sold for the right to reside on the
  Ship.Tens of thousands of species reside in the Great Ship, some
  interacting in the enormous cities and ports, others secluding
  themselves in distant caverns and empty fuel tanks.

(warning, first link is to TVTropes)

