GLENDALE, Ariz. -- Cubs pitcher Carlos Zambrano tuned up for the season at the plate and on the mound, and is preparing for a new chapter in his life as a U.S. citizen.

Zambrano belted his first spring homer, a three-run shot in the second, and added an RBI double in the fourth while pitching five innings in the Cubs' 12-3 win over the Los Angeles Dodgers on Tuesday.

Koyie Hill had four hits, including a two-run homer, and Reed Johnson had three hits, missing the cycle by a home run, for the Cubs, who played in front of a Cactus League record crowd of 13,046 at Camelback Ranch in Glendale.

This was Zambrano's fourth spring game, which includes four innings against Team Japan in an exhibition game last Thursday. He gave up two runs, three hits, two walks while striking out one. He didn't want to talk about his 2-for-3 day at the plate.

"Let's talk about pitching -- that's my business," Zambrano said. "Sometimes you get lucky when the pitcher hangs you a breaking ball. My main job is to pitch, and I did a good job today. Thank God I was feeling good today and did my job today."

He dropped about 15 pounds this offseason and looked more agile on the bases in the fourth, when he sprinted to third on Alfonso Soriano's fly ball to left. His four RBIs will be wiped off the stat sheet on April 6, when he takes the mound to open the season against the Houston Astros.

The upcoming baseball season will become secondary in June or July, when Zambrano hopes to complete the process to become a U.S. citizen. He and his wife, Ismary, have nearly finished the paperwork required for themselves and two of their daughters. One of their daughters was born in the U.S.

"We stay here in the United States most of the time," Zambrano said. "Now that my daughter's getting big and will be a teenager in a year and a half -- I think I'm getting old."

His oldest daughter, Carlis, is 8 1/2 and will be going to school in the Chicago area. Zambrano said when she turns 10, she's considered a teen by Venezuelan standards. Will she be driving a car soon?

"I don't think so," Zambrano said, laughing. "I always tell her, 'You're by yourself when you're 21. Before 21, you're under my control.'"

Sounds like every parent.

Even if Zambrano spends most of his time in the U.S., he hasn't abandoned his homeland.

"That doesn't mean I won't go to Venezuela," Zambrano said. "I'll go to Venezuela for a week, but most of the time I'll spend the rest of my career here."

Maybe he could pitch for Team USA in the next World Baseball Classic?

"No, I'm a Venezuelan," Zambrano said. "I'm proud to be a Venezuelan. I won't be like A-Rod."

A-Rod, a.k.a. Alex Rodriguez, played for Team USA in the 2006 World Baseball Classic but was to play for the Dominican Republic this year until sidelined with a hip injury.

Back to the Cubs and Zambrano. He has delayed Lasik surgery on his right eye until after the regular season ends. He's got other things to focus on, like the 2009 regular season. And even though he doesn't want to talk about hitting, he did volunteer to back up at first base for the Cubs.

"I can play first, left, right," Zambrano said. "I'm available for Lou [Piniella]. If he wants to have a deep bench, he can put me on the bench."

Well, Zambrano is 1-for-6 as a pinch-hitter, and batted .337 last year in his starts. Maybe he could be a designated hitter? It's a thought.