  We consider the properties of a self-avoiding polymer chain, adsorbed on a
solid attractive substrate which is attached with one end to a pulling force.
The conformational properties of such chain and its phase behavior are treated
within a Grand Canonical Ensemble (GCE) approach. We derive theoretical
expressions for the mean size of loops, trains, and tails of an adsorbed chain
under pulling as well as values for the universal exponents which describe
their probability distribution functions. A central result of the theoretical
analysis is the derivation of an expression for the crossover exponent $\phi$,
characterizing polymer adsorption at criticality, $\phi = \alpha -1$, which
relates the precise value of $\phi$ to the exponent $\alpha$, describing
polymer loop statistics. We demonstrate that $1-\gamma_{11} < \alpha < 1 +
\nu$, depending on the possibility of a single loop to interact with
neighboring loops in the adsorbed polymer. The universal surface loop exponent
$\gamma_{11} \approx -0.39$ and the Flory exponent $\nu \approx 0.59$.
  We present the adsorption-desorption phase diagram of a polymer chain under
pulling and demonstrate that the relevant phase transformation becomes first
order whereas in the absence of external force it is known to be a continuous
one. The nature of this transformation turns to be dichotomic, i.e.,
coexistence of different phase states is not possible. These novel theoretical
predictions are verified by means of extensive Monte Carlo simulations.
