Thanks to help on the browserify project on Github, I have an answer for this. Renée Kooi pointed me in the right direction. They said:

If you have multiple entry points, all of them are executed, but browserify doesn't merge modules, which could cause bad unexpected behaviour.

The solution is to have a single file that acts as an entry point for Browserify that exports everything you want exported. Use that single file as your input source file in the entries option. Browserify will walk your app's dependency tree and include the dependencies it requires. Anything exported by the entry point file will be included in the exported module as expected.

A complete example follows. main.js is the entry point file.

a.js

export function fromA() {
    console.log('Hello from a.js');
}

b.js

export function fromB() {
    console.log('Hello from b.js');
}

main.js (This one is new)

export * from './a.js';
export * from './b.js';

gulpfile.js

const browserify = require('browserify');
const gulp = require('gulp');
const log = require('gulplog');
const plumber = require('gulp-plumber');
const source = require('vinyl-source-stream');

function minimalExample(done) {
    return browserify({
            entries: [
                './src/main.js'  // THIS LINE HAS CHANGED FROM THE QUESTION
            ],
            standalone: 'TestModule'
        })
        .transform('babelify')
        .bundle()
            .on('error', log.error)
        .pipe(source('minimalExample.js'))
        .pipe(plumber())
        .pipe(gulp.dest('./dist'));
}

module.exports = {
    minimalExample
};

Now when you run the minimalExample task with gulp, the file generated will have both TestModule.fromA() and TestModule.fromB() functions.

I think your question is about the size of the bundle file (the resulted file of browserify build), you worry about the time it will take when loaded on the page. This is some really important things you should know : 1. you don't have to include all your files in one bundle : you can generate multiple bundles. For example, you can configure browserify to create one bundle for your vendor files, and one or multiple bundles for your components.

1. in Dev mode, you don't have to minify your bundle,

2. For prod, you should generate your bundle using the react prod mode and minification.

To achieve point 1 (multiple bundles), here is an example with grunt browserify plugin.

var jsFiles = {
        jsSrcFiles: './src/main/js/vs/**/*.js*', // my js and jsx source files
        jsLibs: [
            // vendor libs that I want to put in separate bundle
            'react/addons',
            ...
        ]
    };
    ...
    browserify: {
            app: {
                options: {
                    transform: ['reactify'],
                    extensions: ['.jsx'],
                    // Here is where I tell browserify not to bundle vendor files with my source files
                    external: jsFiles.jsLibs

                },
                src: [jsFiles.jsSrcFiles],
                dest: buildParams.js + '/vs_app.js'
            },
            // here is where I build vendor files in separate bundle named vendor.js
            vendor: {
                src: ['.'],
                dest: buildParams.js + '/vendor.js',
                options: {
                    alias: jsFiles.jsLibs
                }
            }
        }...

Browserify is a great tool when it comes to small projects, when your project becomes more complex, browserify config tends to be very complex. In order to have more control of your built bundles, I recommend to use webpack, which is also a tool that facebook recommends. It allows easy bundling customization...

Found it after some more messing around, I add this line to simple.js :

module.exports = { 'Square':Square, 'Cube':Cube };

Then I use browserify with a standalone symbol like this:

browserify simple.js --standalone myFuncs > myfunctions.js

And now I can include myfunctions.js in the HTML file, and use the functions from within JavaScript like this:

var x = myFuncs.Square(3);
var y = myFuncs.Cube(5);