The family of Phillip Hughes would like next week's first Test between Australia and India to go ahead, according to South Australian Cricket Association chief executive Keith Bradshaw.

Addressing the media at the Adelaide Oval, Bradshaw said the South Australian players were "devastated" and that attention would now turn to the welfare of Hughes's former teammates as well as his family.

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"There really are no words that we can use to express or feeling of loss and hurt at the moment," he said.

"The players are devastated. They are shattered.

"Phillip was a popular, loved member of the team. They are trying as best they can to come to terms with this tragic loss. We are obviously supporting them through that with professional help, and it's an hour-by-hour, day-to-day process at the moment.

"Our attention now turns of course to the care and the love of Phillip's family, but also to our staff, to the players here in South Australia and around the country, the Australian cricket team and of course the New South Wales team."

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"Phillip was loved by us all. He was a remarkable talent and he was a remarkable person.

"Last night through the tears and through the emotion, there were many stories that emerged of Phillip's feats on the field, and those stand for themselves and have been reported.

"There are also many stories about his love for cricket, and I would like to mention his remarkable performance too, off the field; in the short time that he was with us here in South Australia, he attended hundreds of clinics where he coached many of our children.

"He loved doing that, he had a real passion for that, and I have to say that the children loved him too. They looked up to him, and he was their hero, and he will live on in their minds, as he will in ours, forever."

Bradshaw said that the Hughes family had expressed their wishes for the Test match to be played, though he felt it was ultimately a matter for the players involved.

"In regard to the Test match, (I can) only (speak) in terms of what I've heard, which is that the Hughes family are keen for that to go ahead," he said.

"Obviously that's going to be a question for the players and we must be mindful for the players and respect the players' feelings at this time as they come to try and deal with this tragic loss."

The SACA have also made the decision that South Australian grade cricket will not be played this weekend.

"There is just so much emotion and distress here at the moment, so grade cricket will not be going ahead this weekend," he added.

"Cricket, everything else is just secondary at the moment to caring for our players, the family, and all those people that have been involved.

"And we'll just do everything we can to care for them and love for them, and make sure that they're as OK as they possibly can be."

Redbacks batsman Tom Cooper, who was housemates with Hughes and was also at the non-striker's end when the batsman suffered his fatal injury, was one of many players grief stricken by the tragedy.

"I spoke to him again this morning," said SACA high performance manager Tim Nielsen.

"He went back up to Sydney yesterday to be as close as he could to his mate and to a few friends he has there.

"He's getting through it.

"It's been tough for him, and tough for us all, but the nice thing is that he's got a lot of mates around here that'll jump in tight and look after him, and I'm sure with all the support we can provide, he'll be OK."