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#Java 7, 145 bytes

Boolean c(int[][]a){int l=a.length;if(l<1)return null;for(int x=1,p=a[0].length;x<l;x++){if(p!=a[x].length)return 0>1;p=a[x].length;}return 1>0;}

NOTE: Since Java can't have multiple different return-types, I settled by using a Boolean. It now returns null when the list is empty. (I suggest not restricting output like this to allow more programming languages to enter the challenge next time..)

Ungolfed / test code:

Try it here.

class Main{
    static Boolean c(int[][] a){
        int l = a.length;
        if (l < 1){
            return null;
        }
        for (int x = 1, p = a[0].length; x < l; x++){
            if (p != a[x].length){
                return 0 > 1; // false
            }
            p = a[x].length;
        }
        return 1 > 0; // true
    }

    public static void main(String[] a) {
        System.out.println(c(new int[0][0]));
        System.out.println(c(new int[][]{ new int[]{1}, new int[]{1}, new int[]{2} }));
        System.out.println(c(new int[][]{ new int[]{1} }));
        System.out.println(c(new int[][]{ new int[]{1,2,3,4} }));
        System.out.println(c(new int[][]{ new int[]{1,2,3,4, }, new int[]{2}, new int[]{12,314123} }));
        System.out.println(c(new int[][]{ new int[]{1,2,3,4}, new int[]{1} }));
    }
}

Output:

null
true
true
true
false
false