By Lawrence Hurley and Andrew Chung

WASHINGTON, Oct 6 (Reuters) - In the likely event that Supreme Court nominee Brett Kavanaugh is confirmed by the U.S. Senate this weekend he will soon be wading into some of the nation's most contentious issues.

Disputes involving abortion, immigration, gay rights, voting rights and transgender troops all could be heading toward the nine justices soon.

There are no blockbusters among the 38 cases already on the docket for the current Supreme Court term, which began on Monday, but justices often add disputes on controversial issues as they are appealed from lower courts.

The Republican-controlled Senate is set for a final vote on Kavanaugh's nomination on Saturday, which could put Kavanaugh on the court as early as next week.

Several legal battles are currently being fought over state laws restricting abortion, including one in Arkansas that effectively bans medication-induced abortions. The justices in May opted not to intervene in a case challenging that law, waiting instead for lower courts to rule, but it could return to them when that happens.

Other abortion-related cases in progress include challenges to laws banning abortions at early stages of pregnancies, including Iowa's prohibition after a fetal heartbeat is detected. There is litigation arising from plans by some states to stop reimbursements under the Medicaid insurance program to Planned Parenthood because of the national healthcare provider's abortion rights stance.

There also are challenges to state laws imposing difficult-to-meet regulations on abortion providers, such as requiring formal ties with a local hospital.

Kavanaugh's judicial record on abortion is thin, although last year he was on a panel of judges that issued an order preventing a 17-year-old illegal immigrant detained in Texas by U.S. authorities from immediately obtaining an abortion. Liberals are concerned, however, that he could provide a decisive fifth vote on the nine-justice court to overturn the 1973 abortion ruling, Roe v. Wade.

In testimony before the Senate during the confirmation process, Kavanaugh called Roe "an important precedent of the Supreme Court that has been reaffirmed many times."

Another issue expected to return to the court is whether certain types of businesses can refuse service to gay couples because of religious objections to same-sex marriage.

The high court in June sided, on narrow legal grounds, with a Colorado baker who refused to make a wedding cake for two men because of his Christian beliefs, but justices sidestepped the larger question of whether to allow broad religious-based exemptions to anti-discrimination laws.