Apple wants the judge who presided over its case against Samsung for egregious copying to tack another $707 million in damages onto the jury’s $1.05 billion verdict and really, really wants a permanent injunction on Korean products that infringe its patents, including Samsung’s new flagship Galaxy S III phone.

Samsung wants a whole new trial claiming the judge threw out too much of its evidence to be fair and that Apple didn’t present convincing evidence of intentional infringement, certainly not enough to warrant treble damages.

It complained that “The Court’s constraints on trial time, witnesses and exhibits were unprecedented for a patent case of this complexity and magnitude, and prevented Samsung from presenting a full and fair case in response to Apple’s many claims.”

It wants “a new trial enabling adequate time and even-handed treatment of the parties.” It at least wants the damages lowered to around $35 million.

It complained about patent law being “manipulated to give one company a monopoly over rectangles with rounded corners, or technology that is being improved every day by Samsung and other companies.”

Apple filed Friday seeking $400 million more for design infringement; $135 million for willful infringement of its utility patents by five phones and two tablets; $121 million in supplemental damages based on Samsung product sales not covered in the jury’s deliberations; and $50 million in pre- judgment interest on damages through December 31. That makes another $707,061,678 for the moment.

It said it wanted an amount that reflects “a rational and fair effort to address Samsung’s willful misconduct that has and will impose lasting harm on Apple.”

It figures “Samsung made a calculated business decision to copy the industrial designs, graphical user interfaces, and touchscreen navigation technology of the iPhone and iPad” and “has reaped extraordinary rewards from its wrongful sale of iPhone and iPad clones by taking market share, revenues and profits from Apple,” adding that the “massive damage to the iPhone’s distinctive product identity caused by Samsung’s sale of millions of iPhone clones is irreversible.”

Samsung is supposed to have 33% of the global smartphone market to Apple’s 17%.

District Judge Lucy Koh may have some answers on December 6. Samsung says it will appeal if Koh rebuffs its demands.

FOSS Patents said the jury ordered Samsung to disgorge profits on products that were found to infringe technical patents and you can only do that under US patent law with respect to design patents. It says an award of $57.9 million will have to be adjusted. Samsung also couldn’t figure out how the jury arrived at damages of $833,076 for the Galaxy Tab 10.1 (WiFi).