What you're asking is more of a "make my div block have the full window or parentDOMElement height" than "how to make ReactComponent have the full window or parentDOMElement height". 
Here's a post that explains this: CSS - Expand float child DIV height to parent's height
The gist of it is that the parent element's position needs to be relative. Then, the child (i.e. the element you're trying to make have a height of 100% of its container) will actually have a height of 100% of its container. 
Here's a demo:
<body>
<div id="title"></div>
<div class="parent">
    <div class="child">
    Hi, I am a child
    </div>
</div>
</body>
<style type="text/css">
    .parent {
        position: relative;
        background-color: rgba(50, 70, 200, 0.3);
        width: 100%;
        height: 200px;
    }
    .child {
        height: 100%;
        background-color: rgba(50, 70, 200, 0.3);
    }
</style>
With that, you just need to Render your React component inside of the .parent div and should work.