Kent were 296 for four in reply to New Zealand's first innings total of 409 at the close on the second day of a four-day tour match at Canterbury on Friday.
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The day belonged to Kent's Robert Key who hit 114 from only 130 balls, a timely reminder to England's selectors who announce on Sunday the squad for the first Test starting next Thursday.
Michael Carberry (72 not out) and Geraint Jones (43 not out) lent able support as the tourists, dominant on day one, had to play second fiddle.
New Zealand started the day on 297 for two after a fine 126 from Michael Papps but struggled to cope with left-arm spinner Min Patel, who ended with five for 56 off 22.3 overs.