Isaac cuddled his daughter, Lila Olivia, 15 weeks old, against his shoulder yesterday, nuzzling her head, and smoothing her little pink flowered dress.

Meredith and Jacki leaped up with their cameras. Proud papa Michael watched from the other side of the picnic blanket spread out at Fort Washington State Park in Flourtown, and Jared, 2, played with his soccer ball nearby.

Maybe you noticed that no one has a last name in this little story, yet it's clearly an intimate gathering - two couples and their children.

That's how it often is at this annual picnic for adopted children and their families held by Adoptions from the Heart, a Wynnewood agency.

Many gather at the picnic for annual reunions of adoptive couples and their children's birth parents. Every family decides, along with the birth parents, how open the relationship will be.

Some families gather by nationality of their adoptive children, with kids from China in one area and families of Russian children at another.

Sometimes you need a cheat sheet to figure out who's who.

Isaac and Meredith, parents of Jared, gave birth to Lila, then Olivia Bella, on Feb. 18, a Monday. By that Thursday, Jacki and Michael were her adoptive parents.

Both couples live in North Jersey and so far they have exchanged e-mails and photos, but not addresses and last names.

Chances are they'll see each other at the picnic next year. "We feel that we now have an extended family," Jacki said.

Fostering open relationships is what social worker Maxine Chalker had in mind when she founded the agency in 1985. Chalker, an adoptee, had successfully searched for her birth mother.

The agency handled 343 domestic and international adoptions last year, including Angelina Jolie's adoption of son Pax from Vietnam.

Neither Jolie nor Pax showed up at yesterday's picnic, attended by about 1,000. Nor were they missed by the kids lined up to have their faces painted, play softball, or just plain visit.

Mark Henry and Vicki Zimmerman have been divorced for 15 years, but they wouldn't miss this picnic - a chance to see their daughter Lola's birth child, Emily, 6, who was adopted by Penny and Joe Lanzisera, of Collegeville.

"We know she's in a loving home," said Vicki Zimmerman. She and Henry brought their new significant others.

"That's one of the kindest things they could have done for our family, to share the love they have for her with us," Zimmerman said.

Lola, who is in her 20s, teared up thinking about her feelings when the picnic ends. "When we first started coming, it was really hard," she said, "but it gets easier every year."

All very serious, but not as important to Emily, and her little sister Claire, 4, also adopted, as a toad hopping on the roots of a tree.

"Every time we meet them and come together, it has felt more and more natural," said Joe Lanzisera.

"There is nothing more in the world that anyone could have done for us that could be better than this," he said.

Lanzisera said that he had qualms about open adoptions. But, he said, he learned they give the children a sense of identity and provide a conduit for important medical information - and little details.

Three generations - Emily, Lola and Vicki - get a stomachache when they eat corn.

Heather and Gwen Fagotti drove up from Pittsgrove with a car full of toys for Heather's birth son, Joshua Walsh, 7, who lives in western New York.

His adoption day "was the most horrible day of my life," Gwen said.

Joshua was 23 months old and living with her because her daughter, Heather, was a drug addict.

Then Gwen got divorced and could no longer care for him because she had to return to work. "I almost had a heart attack."

Shelly Walsh also remembered the day. They had three children and wanted a fourth. "We were so happy, but I was crying for them," she said.

It was just this year that two families exchanged last names. "We've started to share information," Walsh said. "We're easing into it, making sure things are safe. I like our privacy, but I do like to get together."

Heather Fagotti said she was finally free of drug addiction. "I've been struggling since I was 12. Instead of dragging him through the ditch, I loved him enough to have someone else raise him properly and I didn't mess up his head.

"I have peace of mind, seeing that he's good," she said.

Maybe it's all very complicated - whose baby is whose and who carried whom in whose womb and what it means to be a mother and a parent. Joshua, 7, managed to distill it to the essentials.

"I love them both," he said.

Contact staff writer Jane M. Von Bergen at 215-854-2769 or jvonbergen@phillynews.com.