The barrister said: "The circumstances of the offending were as wide and as varied as the defendant's career."
She said that "regardless of who the women were and what they said or did, Brand was not deterred".
"His desire, strong desire, for some form of sexual contact was indiscriminate and voracious," she told the court.
The prosecutor told jurors that Brand would be "nice when he wanted to be, funny - undoubtedly - charming, likeable even, when he wanted something in return".
But she said he would also be "demanding, entitled, a flirt with a huge sexual appetite - childlike in his expectation that his every desire should be met".
The prosecutor said Brand would "appear indifferent, normal and untroubled by what had just occurred" after the encounters.
She added that "sometimes he would leave promptly after the incident, sometimes making an excuse to get away, or sometimes simply continuing as though nothing wrong had happened".
On Wednesday, the jury heard details of the alleged offences.
The first complainant says she met Brand before he was famous in 1999, the jury was told.
She had attended the Labour Party conference and went to a fringe event where she spoke to Brand. He later allegedly raped her.
The prosecution said when Brand was questioned by police about this allegation of rape, "he said if it happened, he didn't remember the incident".
He added that he did not remember the first complainant's name and that he "had never engaged in non-consensual activity".
The second complainant worked for MTV at the time when she says Brand indecently assaulted her.
She said Brand asked her where the toilets were and the woman offered to show him.
When they reached the toilets, prosecutors say, Brand asked the woman to "come in" before grabbing her forearm.
She resisted by struggling and pulling back. He had what she described as a desperate, wild-eyed look on his face, as he said: "Please please come in – oh go on."
The third complainant says Brand orally raped her in a toilet after meeting her at a party in 2004.
Within a minute of meeting, in the middle of a conversation, he lurched forward and grabbed her breasts and squeezed them with both hands, the jury was told.
The prosecution said the woman remembered he had a "big, weird grin" on his face as he did so, then grabbed her arm and pulled her towards the toilets.
The same woman said that as they were driving to another venue, Brand exposed himself, the court heard.
"He said, 'Come on, come on, suck it' – to which she just said, 'No no'," the prosecution added. "He simply laughed but appeared to accept her refusal."
The fourth complainant says Brand pushed her up against a wall at Capital Radio in 2004 or 2005 and kissed her "sloppily and aggressively", and "grabbed her body, at her breasts, sides and buttocks, aggressively".
She was able to push him away and he "just sniggered, like it was a joke", the prosecutor said.
The jury then heard how the fifth complainant says she met Brand when he was performing at the Hammersmith Apollo in London in 2009.
The prosecution said their encounter began with consensual activity, but that he raped her anally on a later occasion.
The jury heard how the woman "spent months and years blaming herself", becoming anxious and unwell.
They were told Brand texted the woman after seeing her at an event the following summer, saying: "I wanna push you further."
She is said to have replied: "I think you pushed me far enough – you treated me like an animal." He allegedly replied: "I'm sorry."
The sixth complainant - who has accused Brand of sexual assault - says he demanded a massage when she was on a work assignment in 2009.
He "fell to his knees and placed his head directly into her groin area", the prosecution said.
After the accounts of the final two women were heard, the prosecutor said Brand told police in 2023 "he has never engaged in non-consensual sexual activity, and that any accounts had been reinvented or imagined after a defamatory documentary and subsequent press reporting".
The trial continues and is expected to last for six weeks.
Brand was accompanied by his wife Laura to the court on Wednesday.
He rose to fame as a stand-up comedian and became a household name as host of TV shows such as Big Brother's Big Mouth, and with his own radio programmes on stations including BBC Radio 2 and 6 Music.
He went on to establish a Hollywood career, starring in films including Forgetting Sarah Marshall and Get Him To The Greek. In recent years, he has turned to podcasting and now lives in Florida in the United States.