How many samples does it take to see all the balls in an urn?

Let an urn contain $N$ balls, numbered from 1 to $N$. A random number of balls are drawn without replacements from the urn, their numbers are noted and the balls are then returned to the urn. This is done repeatedly, the sample sizes being independent identically distributed. Let $v$ be the number of samples needed to see all the balls. A simple approximation for $Ev$ and the asymptotic distribution of $v$ as $N\to\infty$ are obtained.