  Massive black holes are key ingredients of the assembly and evolution of
cosmic structures. Pulsar Timing Arrays (PTAs) currently provide the only means
to observe gravitational radiation from massive black hole binary systems with
masses >10^7 solar masses. The whole cosmic population produces a signal
consisting of two components: (i) a stochastic background resulting from the
incoherent superposition of radiation from the all the sources, and (ii) a
handful of individually resolvable signals that raise above the background
level and are produced by sources sufficiently close and/or massive.
Considering a wide range of massive black hole binary assembly scenarios, we
investigate both the level and shape of the background and the statistics of
resolvable sources. We predict a characteristic background amplitude in the
interval h_c(f = 10^-8 Hz)~5*10^-16 - 5*10^-15, within the detection range of
the complete Parkes PTA. We also quantify the capability of PTAs of measuring
the parameters of individual sources, focusing on monochromatic signals
produced by binaries in circular orbit. We investigate how the results depend
on the number and distribution of pulsars in the array, by computing the
variance-covariance matrix of the parameter measurements. For plausible Square
Kilometre Array (SKA) observations (100 pulsars uniformly distributed in the
sky), and assuming a coherent signal-to-noise ratio of 10, the sky position of
massive black hole binaries can be located within a ~40deg^2 error box, opening
promising prospects for detecting a putative electromagnetic counterpart to the
gravitational wave emission. The planned SKA, can plausibly observe these
unique systems, although the number of detections is likely to be small.
(Abridged)
