  Quantum Monte Carlo (QMC) and Maximum Entropy (ME) techniques are used to
study the spectral function $A({\bf p},\omega)$ of the one band Hubbard model
in strong coupling including a next-nearest-neighbor electronic hopping with
amplitude $t'/t= -0.35$. These values of parameters are chosen to improve the
comparison of the Hubbard model with angle-resolved photoemission (ARPES) data
for $Sr_2 Cu O_2 Cl_2$. A narrow quasiparticle (q.p.) band is observed in the
QMC analysis at the temperature of the simulation $T=t/3$, both at and away
from half-filling. Such a narrow band produces a large accumulation of weight
in the density of states at the top of the valence band. As the electronic
density $< n >$ decreases further away from half-filling, the chemical
potential travels through this energy window with a large number of states, and
by $< n > \sim 0.70$ it has crossed it entirely. The region near momentum
$(0,\pi)$ and $(\pi,0)$ in the spectral function is more sensitive to doping
than momenta along the diagonal from $(0,0)$ to $(\pi,\pi)$. The evolution with
hole density of the quasiparticle dispersion contains some of the features
observed in recent ARPES data in the underdoped regime. For sufficiently large
hole densities the ``flat'' bands at $(\pi,0)$ cross the Fermi energy, a
prediction that could be tested with ARPES techniques applied to overdoped
cuprates. The population of the q.p. band introduces a {\it hidden} density in
the system which produces interesting consequences when the quasiparticles are
assumed to interact through antiferromagnetic fluctuations and studied with the
BCS gap equation formalism. In particular, a region of extended s-wave is found
to compete with d-wave in the overdoped regime, i.e. when the chemical
potential has almost entirely crossed the q.p.
