  We introduce a class of $M \times M$ sample covariance matrices $\mathcal Q$
which subsumes and generalizes several previous models. The associated
population covariance matrix $\Sigma = \mathbb E \cal Q$ is assumed to differ
from the identity by a matrix of bounded rank. All quantities except the rank
of $\Sigma - I_M$ may depend on $M$ in an arbitrary fashion. We investigate the
principal components, i.e.\ the top eigenvalues and eigenvectors, of $\mathcal
Q$. We derive precise large deviation estimates on the generalized components
$\langle \mathbf w, \boldsymbol \xi_i \rangle$ of the outlier and non-outlier
eigenvectors $\boldsymbol \xi_i$. Our results also hold near the so-called BBP
transition, where outliers are created or annihilated, and for degenerate or
near-degenerate outliers. We believe the obtained rates of convergence to be
optimal. In addition, we derive the asymptotic distribution of the generalized
components of the non-outlier eigenvectors. A novel observation arising from
our results is that, unlike the eigenvalues, the eigenvectors of the principal
components contain information about the \emph{subcritical} spikes of $\Sigma$.
  The proofs use several results on the eigenvalues and eigenvectors of the
uncorrelated matrix $\mathcal Q$, satisfying $\mathbb E \mathcal Q = I_M$, as
input: the isotropic local Marchenko-Pastur law established in [9], level
repulsion, and quantum unique ergodicity of the eigenvectors. The latter is a
special case of a new universality result for the joint eigenvalue-eigenvector
distribution.
