  We analyse the polarisation properties of full Poincar\'e beams. We consider
different configurations, such as Laguerre-Poincar\'e, Bessel-Poincar\'e, and
Lambert-Poincar\'e beams. The former is the original Poincar\'e beam produced
by a collinear superposition of two Laguerre-Gauss beams with orthogonal
polarisations. For this configuration, we describe the Stokes statistics and
overall invariant parameters. Similarly, Bessel-Poincar\'e beams are produced
by the collinear superposition of Bessel beams with orthogonal polarisations.
We describe their properties under propagation and show that they behave as a
free-space polarisation attractor transforming elliptical polarisations to
linear polarisations. We also propose a novel type of full Poincar\'e pattern,
one which is generated by a Lambert projection of the Poincar\'e sphere on the
transverse plane, and hence we call them Lambert-Poincar\'e. This
configuration, contrary to the Laguerre-Poincar\'e, provides a finite region
containing all polarisation states uniformly distributed on the Poincar\'e
sphere.
