11:51 AM PT -- A judge just granted Kenneth's request to have internet restrictions lifted as part of the conditions of his pre-trial release. With the court's order now in place, the guy's free to continue surfing the World Wide Web again.
Nicki Minaj's husband really wants to get back to surfing the Internet ... something he's currently barred from doing due to his pending criminal case.
Kenneth Petty just submitted legal docs, obtained by TMZ, begging a California judge to allow him to use the World Wide Web.
As you know ... Kenneth recently registered as a sex offender in Cali aftergetting arrested for allegedly failing to do so when he moved to the state with Nicki. One of the terms of his pretrial release -- he can't use the web unless approved by a supervisor.
According to the docs, prosecutors have already agreed to Kenneth's request ... so now, it's up to the judge to sign off.
Kenneth, who pled not guilty to failing to register as a sex offender, has a curfew and is being required to wear an ankle monitor as he waits for next month's court date. His travel is also restricted to Southern California.