I have some doubts under this topic,
- Can a player aged 19 play under 19 international cricket match? (Since 19 is not under 19)
- Consider a player having birthday during the series/tournament. How the age will be calculated for him?
The age of the player is not determined during the world cup. It is determined on 1st of September before the world cup. E.g. For ICC U19 World Cup 2014 the age of the players was determined based on 1st September 2013. That means any player must be under 19 on 1st Sept. 2013 to be qualified. You can see some players like Vijay Zol, Sanju Samson were over 19 during U19 WC 2014. But they were under 19 on 1st Sept. 2013.
Also to note, maximum age of 19 is applicable for players of Full Member countries only. For players from Associate and Affiliate Member countries the maximum age is 20 (probably due to limited number of cricketers).
To clear the doubt players must be under 19/20 at midnight (in the country of birth). E.g. at changeover from the 31st August to the 1st September.