Polymer ejection from a capsid through a nanoscale pore is an important biological process with relevance to modern biotechnology. Here, we study generic capsid ejection using Langevin dynamics. We show that even when the ejection takes place within the drift-dominated region there is a very high probability for the ejection process not to be completed. Introducing a small aligning force at the pore entrance enhances ejection dramatically. Such a pore asymmetry is a candidate for a mechanism by which a viral ejection is completed. By detailed high-resolution simulations we show that such capsid ejection is an out-of-equilibrium process that shares many common features with the much studied driven polymer translocation through a pore in a wall or a membrane. We find that the escape times scale with polymer length, $\tau \sim N^\alpha$. We show that for the pore without the asymmetry the previous predictions corroborated by Monte Carlo simulations do not hold. For the pore with the asymmetry the scaling exponent varies with the initial monomer density (monomers per capsid volume) $\rho$ inside the capsid. For very low densities $\rho \le 0.002$ the polymer is only weakly confined by the capsid, and we measure $\alpha = 1.33$, which is close to $\alpha = 1.4$ obtained for polymer translocation. At intermediate densities the scaling exponents $\alpha = 1.25$ and $1.21$ for $\rho = 0.01$ and $0.02$, respectively. These scalings are in accord with a crude derivation for the lower limit $\alpha = 1.2$. For the asymmetrical pore precise scaling breaks down, when the density exceeds the value for complete confinement by the capsid, $\rho \gtrapprox 0.25$. The high-resolution data show that the capsid ejection for both pores, analogously to polymer translocation, can be characterized as a multiplicative stochastic process that is dominated by small-scale transitions.