Essex 129 (Cook 52, van der Merwe 3-26) and 257 for 2 (Cook 110, Westley 86*) beat Somerset 209 (Trego 48, Ashar Zaidi 3-17) and 174 (Wagner 6-48) by eight wickets

Those who harboured fears that Alastair Cook would descend into a sea of despond upon conceding the England Test captaincy can rest easy. He is not that sort of man. An unflustered century, following quickly upon his half-century in the first innings, provided an immediate statement in his first match since that his appetite for runs remains as strong as ever and contributed sizeably to Essex's authoritative eight-wicket win against Somerset with more than a day to spare.

On a surface where 18 wickets fell on the second day, only two were taken on the third as Essex, 10 without loss overnight, ticked off their target of 255 with an air of total authority. The break-time larks in the classroom had been stilled the moment the head teacher appeared on the scene: Cook exuded quality from the outset.

By the time he fell, on 110, Essex's victory was as good as assured. Somerset's recourse to desperate measures saw their young captain Tom Abell turn to the occasional left-arm spin of Dean Elgar. His second ball was a long hop and Cook yanked it obligingly to James Hildreth at midwicket. When your first game in charge turns so markedly against you, you probably welcome any luck going.

That apart, as Cook shared stands of 82 with Nick Browne and 134 with Tom Westley, his awkward moments were rare. A missed cut at Jack Leach saw the ball have a nodding acquaintance, no more than that, with his off stump, and, on 95, he played and missed twice in succession at a third left-arm spinner, Roelof van der Merwe, but generally he was at his most orderly, nudging singles square of the wicket, working the leg-side boundary and even unveiling a consummate drive down the ground against Craig Overton - proof that his game was in a good place.

Somerset's task was made harder by a pitch that behaved more genially than on the second day, the loss of pace affecting pace bowlers and spinners alike. "I was quite surprised by the change in the wicket," said Matthew Maynard, Somerset's director of cricket. "It was like taking air out of the ball."

Leach has embedded his reshaped action well enough, but he found little turn or guile; he will hope for that as the season develops. At least he laid down a marker. Dom Bess, the offspinner who impressed alongside him late last summer as Somerset pushed for the title, would arguably have been a more adventurous choice than van der Merwe.

It says much about Cook's equilibrium that he has adjusted to his role back in the ranks so smoothly. He spoke honestly about the transition earlier this month, saying: "It has good days and bad days. It's such a big thing to give away. It's been time to move on as a person and a player."

But a man who does not overly care for the fripperies and the attention that went along with the role of England Test captain can adjust more easily than some as a new county season begins. South Africa lie in wait in July and there is another Ashes series to consider. In the meantime, he will approach each county innings as diligently as ever.

He averaged 91.85 in seven Championship matches last summer, with three centuries, when his England responsibilities also detained him. Essex, back in Division One for the first time since 2010, would accept that as the foundations for their survival.

Not that Essex are embarrassed by his presence, far from it. Their top seven can acquit itself as well as any side at this level. Browne played soundly alongside him until he cut at a short, wide one from Jamie Overton and was done by the bounce. Westley's dapper unbeaten 86 suggested that he can also prosper. Then there is the youthful promise of Dan Lawrence, not forgetting Ravi Bopara, a wonderful law unto himself, who absent-mindedly left his kit at the hotel. He didn't need it; perhaps he knew something we didn't.

Westley, not without England hopes himself, will keep making highly-impressive runs under the Cook shadow. While Cook chose to leave the ground quietly, Westley, not for the first time, satisfied media needs with typical loquaciousness and intelligence. "There are probably not enough words to describe how impressive Cooky is as a person," he said. "He is a phenomenal cricketer. He is relentless as well. He is hungry to score many more runs."

One Cook shot stood out. Jamie Overton, supposedly a potential England fast bowler, tried to rough him up with a bouncer. He caressed it to deep square off his nose end and had so much time that he could have read a copy of Farmers Weekly before he did so. If he has time on his hands these days, that's the sort of time that he will relish most of all.

David Hopps is a general editor at ESPNcricinfo @davidkhopps