— At the end of a full day of more presidential primary contests, the tally showed a familiar pattern: No definitive winner, and no end in sight for the bruising GOP nomination battle.

Former senator Rick Santorum (Pa.) cruised to a victory in the Kansas caucuses with 51 percent of the vote, sweeping all but one of the state’s 105 counties, the Associated Press reported, and bolstering his argument that he, and not former House speaker Gingrich, is the conservative alternative to Mitt Romney.

The former Massachusetts governor’s campaign bypassed the state, and Romney ran a distant second at 21 percent, while Gingrich and Rep. Ron Paul (Tex.) received 14 percent and 13 percent, respectively.

But in the end, only one number counts: 1,144 — the number of delegates a candidate needs to cinch the Republican nomination. And Romney’s campaign claimed victory for the night, collecting 39 delegates overall, to Santorum’s 33. In Wyoming, where some counties had held caucuses earlier in the week, Romney easily outpaced his rivals and won seven of the 12 delegates at stake. Santorum won three, Paul one. (One delegate went uncommitted.)

Earlier, Romney also swept contests in Guam and the Northern Mariana Islands, picking up a total of 18 delegates. The former Massachusetts governor sent his son, Matt, to campaign on his behalf to both territories, making his the only campaign represented in the far-flung Pacific islands.

The true test in that battle will come Tuesday, when the GOP race heads south to two states that should be Gingrich strongholds, Alabama and Mississippi. Polls show a tight race in both states.

Romney began the day with 440 delegates, more than his competitors combined. Santorum had 181, followed by Gingrich with 107 and Paul with 46. By the final ballot counts, Romney had held on to his front-runner perch.

Kansas had 40 delegates at stake Saturday — 12 district-wide delegates for the overall highest vote getter, 25 at-large delegates awarded proportionally based on the statewide vote, and three delegate spots reserved for Republican National Committee members.

All four GOP hopefuls had originally planned to campaign in Kansas. But in a tacit acknowledgment of Santorum’s natural strength there, both Romney and Gingrich decided to bypass the state in favor of campaigning in the South.

That left Santorum battling on the ground against Paul, who drew huge crowds of enthusiastic young people in recent days but whose supporters did not materialize in great numbers on Saturday.

Santorum held three events in Kansas this week, and on Saturday dispatched his wife and son to Wichita, home to one of the state’s largest caucus sites. Karen Santorum received raucous applause for her address, during which she choked up at times when talking about the couple’s 3-year-old daughter, Bella, and hailed her husband as a candidate who is someone who “is not a well-oiled weather vane.”

In remarks to supporters in Springfield, Mo., shortly after the race was called, Santorum noted that he was on his way to winning “the vast majority of delegates” from Kansas. With a new jobs report showing the economic recovery picking up steam, Santorum also recast the GOP race as a fight not solely over economic issues but also over which candidate is best-equipped to face President Obama on foreign affairs and the health-care reform law.

“The issue may not be jobs and the economy,” Santorum said. “It may be something more fundamentally important: Having someone who stood up for something called freedom.”

Romney, meanwhile, was the only candidate who failed to send a surrogate to Wichita. His campaign had not even organized for a volunteer to man the Romney table at the event.

On Tuesday in Alabama and Mississippi, a total of 90 delegates is at stake. In recent days, polls have predicted a close race between Romney, Santorum and Gingrich, who represented nearby Georgia for two decades in Congress.

Gingrich spent much of the previous week zig-zagging across the two states in hopes of reviving his flagging candidacy. He won GOP primaries in South Carolina and his native Georgia but has struggled to gain traction elsewhere.

Those woes have led to calls for Gingrich to withdraw so that Santorum can focus on his battle against Romney without additional competition for votes from the most conservative members of the party. A Gingrich staffer days ago said his candidate needed to win Tuesday’s primaries in order to keep his hopes alive. But Gingrich later insisted that no matter the results, he plans to remain in the race through the GOP’s convention in Tampa this August.

Dennis reported from Washington.