If you wanna pass the state {name:"helloworld"} do it like that:
class App extends React.Component {
constuctor(props)  {
     super(props);
     this.state = {name:"helloworld"};
}
 render() { 
  return( 
   <ChildComponent {...this.state} /> 
  ); 
 } 
}
and in the child component you can do:
<Text>{this.props.name}</Text>
But If you want to pass the props of the component to it's child:
   class App extends React.Component {
    constuctor(props)  {
         super(props);
         this.state = {name:"helloworld"};
    }
     render() { 
      return( 
       <ChildComponent {...this.props} />
      ); 
     } 
    }
and in the child component you can do:
<Text>{this.props.stuff}</Text>//place stuff by any property name in props
Now if you want to update the state of parent component from the child component you will need to pass a function to the child component:
 class App extends React.Component {
    constuctor(props)  {
         super(props);
         this.state = {name:"helloworld"};
    }
    update(name){
       this.setState({name:name})// or with es6 this.setState({name})
    }
    render() { 
     return( 
      <ChildComponent {...this.props, update: this.update.bind(this)} />
     ); 
    } 
  }
and then in child component you can use this : this.props.update('new name')
UPDATE 
use more es6 and removed constructor
class App extends React.Component {
    state = {name:"helloworld"};
    // es6 function, will be bind with adding .bind(this)
    update = name => {
       this.setState({name:name})// or with es6 this.setState({name})
    }
    render() { 
     // notice that we removed .bind(this) from the update
     return(
     //send multiple methods using ','
      <ChildComponent {...this.props, update = this.update} />
     ); 
    } 
  }