Southee and Boult shared seven wickets to bowl WI out for 213, after which the visitors showed some resistance but still stare at an embarrassing defeat.
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Day two roundup: Ross Taylor's first Test double century helped New Zealand to 609 for 9 declared before his bowlers reduced West Indies to 67 for 2 as the hosts took firm control on day two of the first Test in Dunedin .
Taylor produced a controlled 217 not out and combined in a string of productive partnerships to push New Zealand past 600 for just the fourth time in their Test history.
It was their highest score against West Indies, surpassing the 543 for 3 the 1972 team scored in Guyana, and the highest Test score in Dunedin, eclipsing the 586 for 7 New Zealand made against Sri Lanka in 1997.