  (Abridged) We explore the role of X-ray photoevaporation in the evolution and
dispersal of viscously evolving T-Tauri discs. We show that the X-ray
photoevaporation wind rates scale linearly with X-ray luminosity, such that the
observed range of X-ray luminosities for solar-type T-Tauri stars (10e28-10e31
erg\s) gives rise to vigorous disc winds with rates of order 10e-10-10e-7
M_sun/yr. We use the wind solutions from radiation-hydrodynamic models, coupled
to a viscous evolution model to construct a population synthesis model so that
we may study the physical properties of evolving discs and so-called
`transition discs'. Current observations of disc lifetimes and accretion rates
can be matched by our model assuming a viscosity parameter alpha = 2.5e-3. Our
models confirm that X-rays play a dominant role in the evolution and dispersal
of protoplanetary discs giving rise to the observed diverse population of inner
hole `transition' sources which include those with massive outer discs, those
with gas in their inner holes and those with detectable accretion signatures.
To help understand the nature of observed transition discs we present a
diagnostic diagram based on accretion rates versus inner hole sizes that
demonstrate that, contrary to recent claims, many of the observed accreting and
non accreting transition discs can easily be explained by X-ray
photoevaporation. Finally, we confirm the conjecture of Drake et al. (2009),
that accretion is suppressed by the X-rays through `photoevaporation starved
accretion' and predict this effect can give rise to a negative correlation
between X-ray luminosity and accretion rate, as reported in the Orion data.
