  We calculate the full asymptotic expansion of boundary blow-up so- lutions,
for any nonlinearity f . Our approach enables us to state sharp qualitative
results regarding uniqueness and ra- dial symmetry of solutions, as well as a
characterization of nonlinearities for which the blow-up rate is universal. At
last, we study in more detail the standard nonlinearities f (u) = u^p, p > 1
