  We derive a simple expression for the tail-asymptotics of an explosive birth
process at a fixed observation time conditioned on non-explosion. Using the
well-established exponential embedding, we apply this result to compute the
tail distribution of the number of balls of a losing colour in generalized P
\'{o}lya urn models with super-linear feedback, which are known to exhibit a
strong monopoly for the winning colour where losers only win a finite amount.
Previous results in this direction were restricted to two colours with the same
feedback, which we extend to an arbitrary finite number of colours with
individual feedback mechanisms. As an apparent paradox, losing colours with
weak feedback are more likely to win in many steps than those with strong
feedback. Our approach also allows to characterize the correlations of several
losing colours, which provides new insight in the distribution of other related
quantities like the total number of balls for losing colours or the time to
monopoly. In order to give a complete picture, we also consider sub-linear
feedback and discuss asymptotics for a diverging number of colours.
